PRE2019 3 Group16

Group Members

Name	Student Number	Study	Email
Efe Utku	1284290	Applied Physics	e.utku@student.tue.nl
Roel den Hoet	1248170	Computer Science	r.d.hoet@student.tue.nl
Venislav Varbanov	1284401	Computer Science	v.varbanov@student.tue.nl

Problem Statement

Infectious disease outbreaks have been a fundamental threat to humanity since its history. There are various settings, worldwide, that might lead to an epidemic or a pandemic due to bacterial, viral etc. reasons. Although these outbreaks have various impacts on the society; one of them is the failure of health systems. Every region has its own medical capacity; limited by their number of beds, doctors, nurses etc. and during an outbreak, a fast spreading disease may lead to an overwhelming number of patients seeking medical attention. Here, we suggest a drone operation that can be used in viral outbreaks for remote testing and collecting nasopharyngeal specimen from people living in preselected disease-prone regions and communities. By decreasing the effective contact rate significantly and keeping precise track of more people in less time compared to current strategies; we aim to decrease the consequences of an outbreak on the community.

Subject

Communicable diseases can be defined as diseases with the possibility to be transmitted from one individual to another and they can be “classified by a variety of methods: by clinical syndrome, mode of transmission, methods of prevention…”. (Tulchinsky et al., 2014) As, Tulchinsky et al. points out despite the advances in technology and medical sciences; they are likely to remain a challenge for public health. These communicable diseases also affect community life; so, starting from their effects on individuals, in time, they spread over and might cause epidemics/ pandemics. Epidemics are defined as local infectious disease outbreaks that occur in a community or region. Thus, collective problems of each individual start to affect the society altogether. The major impacts of these outbreaks are reflected on the daily life of community members as economical, social and political issues. The economical problems are mostly due to measures taken to prevent the spreading of the disease; e.g. working, transportation and gatherings in public areas are halted, borders are closed, import/ export limitations. Social problems arise from the difficulties faced by the society as economical and state related problems begin to affect masses in time. Inevitably, social tensions lead to political issues and the occasion becomes a positive feedback cycle of problems. An example of a central problem emerging in dangerous situations is the failure of health systems; faster the disease spreads more people need medical attention in the short term. In addition, medical sector, like other sectors, has finite resources and limitations; so, hospitals can be overwhelmed, and health systems might fail to provide adequate attention. “This threat may increase as infectious diseases evolve and escape current human-developed control mechanisms.” (Tulchinsky et al., 2014)

To minimize these impacts states must keep an up-to-date record of regions that are prone, people who might be infected and people who are more susceptible to infections; because in the bigger picture the main problem is fast identification and tracking of reported cases. Only this way, measures and intervention policies can be effectively applied; so, the spreading rate can be reduced and the distribution of new cases per day can be minimized. The most efficient way to do this is to detect “local sources” of an outbreak. These are the people who are not infected by an infectious person inside the community; one can call them “first generation” of infected people. Also, here detection refers to subjecting them to a test which gives positive/ negative outcome indicating their disease status. Then, by reinvestigating the timeline of the sources; the spreading can be blocked to some extent; conditional on the mode of transmission of the outbreak. However, this approach is most of the times too difficult as reinvestigation of the timeline is merely “rational guessing” and some diseases have radically high transmission rates e.g. mostly modelled by exponentials. So, it can be difficult to distinguish between first and secondary cases. Thus, instead of focusing on actual “local sources”, states focus on all cases as being local sources. As time progresses, this also becomes increasingly hard to control due to the number of cases and it has cost and logistic complications within. Because every identification means a test and every test means a possible source going to a hospital, laboratory and contacting crowds including doctors and nurses.

So, we suggest an alternative strategy; to self-collect samples and use aerial drones for specimen collection and case identification. The core aim of the drone operations is to provide a faster logistic solution for case reporting, to increase the number of tests that can be conducted in a day and to make tests more remote, so less people are contacted in the process of testing. Hence, more time is provided to act and take precautions regarding the spread; such as increasing the capacity of hospitals and strengthening the health system.

This subject is going to be investigated in terms of its’ effects on different stakeholders and the its’ numerical impact on the way the disease spreads. The later, technical, part also consists of 2 components. First one is the mathematical model describing the population dynamics with and without the drone strategy, and the second one is an optimization problem to get a realistic point of view on the possibilities of this strategy.

Objectives

Deliverables

The list of the deliverables and their explanations are given below.

Mathematical Model and Simulation of Population Dynamics

An interpretation of the "S-E-I-Q-H-R" compartmental epidemiological model describing the population dynamics of a community. The model is given by a system of ordinary differential equations.

A MATLAB script for simulating mentioned mathematical model; which is used to investigate the impact of the drone operation on the spreading of the disease.

Users

Primary Users

The primary users of our product are the companies that are dealing with a viral outbreak. These companies have to find a good balance between being able to operate while still protecting their employees from unnecessary exposure to the disease. If they try to protect their employees too much, their company profits will suffer from the lack of employees that are still able to work in the company. However, if they let everyone come to work anyways, the employees might infect each other, which also leads to reduced profits. With our project, companies can find the employees in their company that are infected with the disease and isolate them from the rest of the company, while not isolating the employees that are healthy to make sure that the company can still continue making profits when possible.

The other primary users of our products are governments and municipalities that are dealing with a viral outbreak. These users are interested in keeping as many people healthy as possible, by identifying the infected people and isolating them from others. Our product can be used to keep the amount of infected people to a minimum while avoiding a complete lock down situation. If the infected people are found quickly, the impact on the healthy part of the population can be very low. By targeting the people that are most susceptible to the disease first, our product can stop the spreading of the disease in an early state.

Secondary Users

The secondary users of our product are the people that will be tested by their company or government. For the people that are susceptible to the disease, our test can either give them confirmation that they are indeed sick, in which case they need to stay home to avoid infecting other people, or it can tell them that they are not yet infected by the disease, in which case they can safely go outside without having to worry about infecting other people. This can make the infection rate much lower, as asymptotic people can also be identified in this way. Without this test, the asymptotic people would go outside and infect other people without knowing that they are sick.

Society

For more than 500 years, big epidemics have killed millions of people from all over the world. These epidemics do not only harm the people directly, but also damage the economy wherever they strike. The influenza epidemic from 2009 caused more than one billion dollar in damages to the economy of the United States (ref https://doi.org/10.3109/00365548.2012.749423), which included medical costs but also indirect costs of this epidemic. For society, the impact on people's lives during such epidemics are massive. Normal daily life becomes almost impossible during this time due to governmental lockdowns and the fear of being infected while outside. With our project, we want to limit the impact of an epidemic outbreak on normal daily life by quickly finding the people that are infected and isolating them from the healthy people to decrease the spreading of the disease. This does not only apply to the people that are showing symptoms of the disease, but also to asymptotic people, who are infecting healthy people without knowing that they are sick.

Description of the Operation

Pre-Test Phase

Selection

This phase is as essential to the operation as the testing phase is. Because, the success of the whole operation is dependent on the sample group of people who are tested. Testing of regions and areas that are not of neccessary would lead to wasting of resources. Considering the resource limitations of epidemics/ pandemics, the reflection of these wasted resources on the society would be of critical importance. So, the goal of this phase is to optimize the usage of resources by limiting the operation zones. Only by this way the overall success of the tests would be greater, so more people can be isolated and identified as exposed/ infected.

There are methods to evaluate how prone a region is both prior to the outbreak and during the outbreak. Both would require huge amount of data processing and AI and ML solutions would be required. As these techniques are not in the scope of this project, they are not going to be discussed in detail, but this section will serve as an outline to list the possibility of such methods.

A major approach to this issue is to use “Predictive Analysis” and more specifically “Health Predictive Analysis”. Ibrahim et al. (2017) gives a fine descriptive framework by evaluating the factors leading to spreading of diseases. They identify 4 main categories to start from; physical network, geography, clinical studies and social media. They also argue about the correlation of these categories and how they relate to “dissemination factors”. The drone operation will start in case of an outbreak and act as a local solution. It can also be used simultaneously in multiple regions to be considered as a global solution. Thus, the geography category can be neglected as it is the category related to ecological factors such as temperature and humidity. Because, the operation area can be seen as having homogenous ecological features. As to prioritize the other categories regarding the scope of the drones, we consider “physical network” to be the most important factor. Physical network refers to features such as population density. Andrick et al. (1997) point out that viruses need a third-party aid to mobilize themselves and to infect another host. This statement emphasizes the importance of physical contact and especially “effective contact rate” which is a direct parameter in the mathematical model. Second important category is “clinical studies” which outlines the awareness of districts and neighbourhoods regarding outbreaks and health care. This category can also be thought as a probability of how likely an individual from a specific zone can be infected and infect other people. The last category is social media which uses factors like geo-mapping. This can be seen as an additional category for real time double-checking of the contagion. It utilizes social media activities of areas and can be modelled easily by the ratio of “Negative Update Posts” to “Total Number of Live Feed” according to Ibrahim et al..

The data related to these categories can be collected in a periodic fashion to form databases by the help of national governments and private companies. The next step is to process the data. Gakwaya et al. (2019) proposes several methods to do so; Likelihood, Improved Expectation Maximization and Ensemble Neural Networks. For the sake of this project we consider the latter to be the appropriate one. “Ensemble classifier is a ML technique, which has been used to learn and recognize complex patterns.” In their paper they give an illustration of the algorithm for Ebola virus, it can be extended to SARS-CoV-like diseases in our case. It takes a definition of the virus as an input which are the classifiers mentioned in the previous paragraph. Then, the data is processed in two categories, “confirmed cases” and “suspected (unconfirmed) cases”. The yield can be used identify prone regions and, by updating the data regularly and including new cases, it can be used to identify suspected people to be tested .

In addition, there are several symptomatic criteria to identify individuals as probable cases. People matching these criteria can also contact the authorities performing the operation, in request to be tested. The major symptoms for SARS-CoV include: “persistent fever, myalgia dry cough, headache and dyspnoea” (Hui et al., 2003). If they also have a history of possible “effective contact” they may qualify. Otherwise, the requests for tests can exceed the test kits in the repository.

After people are identified to be tested using these methods, they can be informed by calling or by other means of communication like phone applications. Although, we don’t actually propose a way to inform people for now, we sketch a few possibilities. This is because not everyone can be accessed in the same way; for example, there are people without smart phones. However, it should be noted that application usage is our preferred way as it can also be used to notify people regarding their test results and update them on daily basis by giving recommendations (suspected areas, health care routines etc…).

Operation Bases

The construction and preparation of the operation bases is also a procedure that needs to be performed before the start of testing phase, as the facility needs to be ready for processing any sample that they receive; and after the selection of regions/ people that are going to be tested because the location of the bases are selected accordingly. The selection of bases' location is treated as a logistic problem and solved using optimization algorithms. By this way, most suitable locations can be identified to achieve the fastest working specimen transportation/ testing routes. The need for number of bases increases with the estimated number of tests that will be performed and also affected by the topography and complexity of the terrain/ urban environment.

The bases can be formed using pre-fabricated building techniques, companies such as CID Steel Building, Inc. and PortaFab and Vanguard Modular provide such capabilities under the name "modular laboratories" and also offer different sizing and configurations. Another advantage of using pre-fabricated structures is the possibility to relocate them; meaning once they are constructed and used in an outbreak, they can be stored to be used in another situation. In addition companies like STARRCO can also provide "isolation rooms" and "negative pressure rooms", which are vital for disease outbreaks as they can transform the same facility to an "emergency hospital". This feature is especially critical in epidemic/ pandemic times when there is high demand for hospital beds.

Another need of the bases is the actual machines that perform the testing. There are a variety of techniques and machines that can be used, each having different duration, sensitivity, efficiency and ultimately price. ThermoFisher Scientific is one of the many companies providing these equipment. They have different options for versatility, sensitivity, efficiency etc... In the scope of this operation we think the most suitable machines would be "QuantStudio 12K Flex Real-Time PCR System", "StepOne™/ StepOnePlus™ Systems" and similar Real Time RT-PCR machines. The latter one is considered to be more productive in terms of simple-usage, duration and price; which is needed for fast test processing and increasing the number of daily tests. It is also easy to transport and configure considering its' 24kg weight and dimensions.

"A photo of StepOnePlus System"

Test Phase

How Sampling is Performed

After notifying the selected people that they are going to be tested, an empty container with the right apparatus is sent to them prior to the collection. The container has a QR code representing the individual/ household. Normally, the containers are marked by waterproof pen; however, that might lead to confusion in the automated process of sample collection, so it is not used. The type of test and the size of the container depends on the outbreak, as different specimen and different test are needed for different diseases. In this project we are going to focus on viral outbreaks and more specifically SARS-CoV-like diseases. For such diseases, methods like PCR tests, negative antibody tests and virus isolation are currently approved and used by WHO. Also, it should be noted that each test has different procedures and confirmation times. RT-PCR methods are confirmed within 3-4 hours whereas virus culture methods can last 2-10 days. Each test has their own sensitivity, time and effectiveness implications for the whole drone operation.

So, depending on the disease, in this case mostly upper respiratory nasopharyngeal swabs are collected and processed. This sampling is also assumed to be the most effective sampling regarding the operation as it has relatively higher sensitivity for self-collected specimen. This is also noted by Jackson et al. as “self-swabbing at home is feasible for confirming Acute Respiratory Infection etiology” according to a 2015 study. The instructions regarding the collection procedure is also sent along the empty container to clarify any misunderstanding. An example text presented in the CDC website is as follows:

“Insert a swab into nostril parallel to the palate. Swab should reach depth equal to distance from nostrils to outer opening of the ear. Leave swab in place for several seconds to absorb secretions. Slowly remove swab while rotating it.”

According CDC, the specimens must be stored in a 2 to 8 degrees Celcius environment and the sensitivity of the test is maintained up to 72 hours in such conditions. During the transportation ice packs can be used to suffice this condition. Otherwise, -70 degrees Celcius cryogenic usage is recommended; which is not possible in non-medical facilities. The samples are then collected and transported to the selected clinical facility, base.

Approach and Return of Drones to Bases

On the day that the person is supposed to get tested, they get a notification from a phone application. This notification tells them that a drone will visit them today to collect specimen. A few minutes before the drone arrives, they get another notification that the drone is nearby. When the drone has arrived, the people will put their specimen in a plastic container marked with a QR code and their name. The drone will wait at the door until all specimen from the household is collected or until x minutes have passed since its arrival. The drone then leaves and flies to the next destination, either another person or the operation basis.

Drone (State of the Art)

The drones that are available on the market can be divided into several categories, each with different price ranges and different uses. The drones under €500 are usually toy drones that should not be used for professional work, so for this project they are not interesting to look at. Drones that are more expensive are usually used by professionals, with high quality cameras and more intelligent flying options. There are a lot of options in different price ranges here, such as the DJI Mavic 2 Pro (https://www.dji.com/mavic-2) for about €1500 and the Intel Falcon 8+ (https://www.intel.com/content/www/us/en/products/drones/falcon-8.html) for about €30,000.

For our project, we need a drone with a good battery that can fly in a city environment autonomously without any problems. The drone should also be able to carry the specimen containers safely to the operation basis. The drone with the highest flight time is the DJI Mavic 2 Pro, which can fly for 30 minutes at 25 kilometers per hour. For our project, this would mean a maximum range of 6.25 kilometers from the drone base where we can operate. However, this drone is not made for carrying objects.

Drones that are made for sample transportation, like the Matternet M2 (https://www.engineeringforchange.org/solutions/product/matternet-m2/), which can carry a payload of 1 kilogram for a maximum of 20 kilometers, are more interesting for our project, since these drones are made for the same purpose as the drones we need. This drone also fits the requirement of being able to fly autonomously to the destination. These drones can carry a maximum payload of 2 kilograms, but carrying more than 1 kilogram will negatively impact the range of the drone on a single battery charge. The drone uses GPS and other sensors to find its way to the destination given by the user.

Population Dynamics

Mathematical Model

Use of mathematical methods have proven to be a successful way for estimating population dynamics. This approach dates back to mid 18th century and Bernoulli’s works on smallpox. He is also the first one to clearly define some of the most crucial epidemiological parameters, which are still used now. (Dietz, 2000) Although these methods are being improved since then, his work has also been essential to the theory of disease control. (Smolinski et al., 2003) Disease control theory refers to the applied intervention policies regarding infectious diseases and their systematic study as mathematical models. These models, consisting of various parameters, provide the framework to investigate how each intervention policy will affect the dynamics of population groups in case of an outbreak.

Based on the drone operation intervention policy mentioned in this report; here, we propose a compartmental epidemiological model to study the impact of this strategy. Compartmental models are deterministic, helpful for simplifying the problem and hold an assumption that individuals in the same compartment have the identical characteristics; thus, mean values are used. The model we used is derived from the iconic “S-E-I-R” Model (Kermack et al., 1927), the model used in the study of Chowell et al. on early detection of Ebola virus and "S-E-I-Q-H-R" model of Safi et al. (2010) whose results are complementary to the core aim of our approach

We define a model where the population is divided into 6 compartments. Namely; Susceptible (“S”), Exposed (“E”), Infected (“I”), Quarantined (“Q”), Hospitalized (“H”) and Recovered ("R").

Susceptible group, S(t), is the people who can be infected at time "t", Exposed group is people who are infected but are asymptomatic, can't infect other people and can give positive test results, Infected group is the people who can infect other people and symptomatic. Quarantined people are the group that is identified as positive carrier of the disease, might be symptomatic or asymptomatic and can infect other people to some extent depending on the effectiveness of the quarantine; Hospitalized people are people who are infected and as a consequence of their condition need medical attention. Finally, Recovered people are the group who were infected and recovered from the disease after some time. It should be noted that in the model a parameter is used to describe the fraction of people who can become susceptible after recovery; yet, considering our case study SARS-CoV-like diseases; this transition is neither experimentally verified nor proved to be impossible.

The flow diagram of the model given below displays the transitions between the states.

And the corresponding differential equations are given as;

dS / dt = Π + ψR - λS - μS,

dE / dt = λS - (κ+σ+μ)E,

dI / dt = κE - (γ1+φ+μ+δ1)I,

dQ / dt = σE - (α+μ)Q,

dH / dt = αQ + φI - (γ2+μ+δ2)H,

dR / dt = γ1I + γ2H - (ψ+μ)R.

Where;

λ(t) = β(I+ηH)/ N

is defined as the “force of infection” by Safi et al..

μ, Π, κ, α, φ, ψ, δ1, δ2, η, γ1, γ2, β and σ are consecutively the natural death rate, recruitment rate, rate of development of clinical symptoms, hospitalization rate of quarantined (Q), hospitalization rate of infected (I), loss of infection acquired immunity, death rate of I, death rate of H, relative infectiousness, recovery rate of infected people, recovery rate of hospitalized people, effective contact rate and rate of being quarantined. The values of the parameters are defined such that they reflect the SARS outbreak of 2003.

In addition, the parameter σ is redefined to be proportional to the maximum number of tests that can be conducted in a day and the sensitivity of test. The sensitivity of the test is also a function of the sensitivity of the sample being used in the test. As the sample is self-collected it has uncertainty and that is written in accordance with the results of Jackson et al.(2015).

The model has the boundaries: (S(0),E(0),I(0),Q(0),H(0),R(0)) ∈ { (S,E,I,Q,H,R) ∈ [0,N^6 ]: S≥0, E≥0, I≥0, Q≥0, H≥0, R≥0, S + E + I + Q + H + R = N }

From these boundaries, in the limit t→∞ it can be proven that a Disease-Free Equilibrium and an Endemic Equilibrium exists for different initial conditions. More information regarding the global dynamics of the model is present in Safi et al. 2010 paper.

Significance of the Model

There are various epidemiological models present in literature. The reason for selecting this model is its approach to the impact of intervention policies. Safi et al. claim quarantine and isolation of individuals is "probably the first infection control measure in the history" and it has been proven to be successful in numerous "emerging and re-emerging human diseases" including plague, cholera, ebola, pandemic influenza... Gumel et al. (2004) also used variety of this model in their paper "Modelling Strategies for Controlling SARS Outbreak" right after the SARS outbreak of 2002 where more than 30 countries and regions were affected. So, it is a widely accepted model to demonstrate the impact of these control measures.

Our use of the model, however, varies from these studies in terms of the proportionality of some parameters. We use this proportionality to show the difference our drone based testing approach has in relation to the current testing approaches. First difference is due to the number of tests; by providing a faster logistic solution we assume that more tests can be conducted using a drone fleet. Increased number of tests is reflected in the rate in which individuals are quarantined. Because more tests mean more identification and faster application of the isolation measures. The second difference is related with the remote testing opportunity our approach provides. As potentially infected people go to the nearest laboratory, pharmacy or hospital to be tested, they might use public transport or any means of transport to go to the institution. Also in the institution they might wait in lines and contact with other susceptible people. So, in the best case scenario they only contact the doctor, nurse, medic and there comes the risk of infecting a medical personnel. Considering the incubation period of the disease, this risk is enhanced in each contact involuntarily. As to reflect this risk in the model, we vary the "force of spread" function. There, the parameter referred as the "effectiveness of isolation" counts for this effect. 0 means this risk is minimized and 1 means none of the remote testing strategies are used.

Furthermore, the models can be extended to include different kinds of tests. Different tests have different verification periods as mentioned, this property can be applied as a factor of the quarantine rate as well. In the operations and numerical analysis elaborated on this project, the tests are assumed to be RT-PCR methods that give results in the same day. Thus, the mentioned factor is taken as "1".

Model Parameters and Case Scenario

For the interest of the simulation a case scenario is identified. The parameters below aim to reflect a scenario of a SARS-CoV-2 outbreak in the Netherlands. Some values from the SARS outbreak of 2003 are used as studies indicate vast similarity between two diseases and they’re from the same family of Corona viruses. As there are many relatively-less population density regions and towns are present in the Netherlands and the drone operations are performed locally; the numerical simulation focuses on the population dynamics of a region of “20000” people. This value is also influenced by the statistics that 265 of 288 Dutch cities have a population in between 10000 and 100000. Furthermore, it is assumed that all the requirements of the mentioned drone operation are fulfilled; e.g. bases are formed in time, testing equipment is sufficient, all tests can be collected/ transported safely. Also; the population is homogenous meaning effective contact rate and other characteristics are same for every individual, and sensitivity of the testing procedure is constant (age-of-infection is not used).

The selected constant parameters and their values are below.

Initial Population = 20000

Π = 0.0101 * 20000 = 202; Calculated by the product of birth rate in Netherlands (2020) and the Initial Population.

μ = 0.0089; The mortality rate in Netherlands (2020)

κ = 0.156986 (Donnely et al., 2003)

α = 0.156986 (Donnely et al., 2003);

The above two values are of a Honk Kong study as no data could be found about Netherlands.

φ = 0.20619; (Chowell et al., 2004)

ψ = 0.001; No data is present about infection acquired immunity; however, absence of evidence does not indicate evidence of absence. Thus, an uncertainty factor of 0.01 is used.

δ1 = 0.04227; (Leung et al., 2004)

δ2 = 0.027855; (Chowell et al., 2004)

γ1 = 0.03521; (Chowell et al., 2004)

γ2 = 0.027855; (Chowell et al., 2004)

Mean contact rate = 0.9575; Calculated by the weighted average of contact rates of different age groups living in the Netherlands. The contact matrix data is gathered from S.5 Appendix of Mossong et al. (2008)

β = Mean contact rate * Transmission Risk;

Transmission Risk = 0.20; Estimated according to the present data on β values of investigated models.

Sensitivity of the test = 0.70; (Al-Tawfiq et al., 2020)

Sensitivity of the sampling = 0.782; (Jackson et al., 2015)

Below are the parameters that can be varied to investigate the impact of different strategies.

Duration of a single test = 1; Real Time RT-PCR methods and rapid diagnostic kits are assumed to be used.

Testing Rate = (T/N) * Duration of a single test;

Testing rate is defined as the number of tests divided by the total population (T/N) times the duration of a test. It reflects the maximum number of tests that can be performed rather than daily test number. In example, testing rate of 1 implies everybody is tested everyday. As of March 25, 2500 daily tests are being conducted in the Netherlands. T/N = 2500/17180000 = 0.00014552.

σ defined as: Sensitivity of the test * Sensitivity of the sampling * Testing Rate;

η as the effectiveness of isolation e.g. 0=perfect intervention;

Results of the Simulation

In this section, several scenarios obtained for spreading of SARS-CoV-like diseases in the Netherlands are numerically simulated using MATLAB and the initial conditions above. These scenarios display the impact of in-house testing strategy on the spreading of the disease. In addition, number of acute care beds is also displayed in the graph to get a view of the bigger picture. According to the latest OECD data, Netherlands has 3.32 beds for 1000 inhabitants.

First Scenario: Varying η for Evaluating Remote Testing

As more people are subjected to tests in their house, the relative infectiousness presented in the "force of spread" is varied between 0.2 and 1 with incrementation of 0.2. Although empirical evidence is required to understand the exact impact and select a definite value; varying the η parameter demonstrates the impact and significance of the proposed strategy.

Furthermore, the initial conditions are based on the emergence of Covid-19 in the Netherlands. According to RIVM, 6412 identified cases were present on 25 March. Thus, 6412/17180000*20000 = 7.4645 is rounded towards positive infinity and the initial value for Infected group is selected to be 8. As a result,

S(0) = 19992,

E(0) = 0,

I(0) = 8,

Q(0) = 0,

H(0) = 0,

R(0) = 0 are the initial conditions.

Above figures show how different η values affect the overall distribution of each group where the other parameters are held constant. With top left being η = 0.2, top right 0.4, middle left 0.6, middle right 0.8 and bottom 1. It can be seen that lower &eta’ values reduce the transmission speed of the disease and yield lower peak values for E(t), I(t), Q(t) and H(t). Also, low η values shift the peak away from the origin, meaning the peak value is reached in a further date. As a result, the curve flattens. Top left graph also demonstrates for critically low η values the transmission rate is quickly damped and the chance of an epidemic is eliminated.

The figure on the left compares the H(t) values of each η value (from left peak to right; 1, 0.8, 0.6, 0.4 and 0.2) and the straight blue line shows the bed capacity of hospitals for a population of 20000, which is 66.4. η values higher than 0.2 always overshoot this capacity for these initial conditions. It is not clearly visible, yet the green curve below is the occasion where η is 0.2. In addition; the curves overshooting the bed capacity, in reality will be steeper and sharper as the effect of this overshoot is not represented in the model. Once this limit is exceeded, the needed attention can’t be given by the medical personnel causing more mortality and failure in the health system. A recent example would be Italy in 2020 Covid-19 pandemic. It must be noted that this evaluation is based on the assumption that no additional measures are taken, as in reality the product of this occasion would be far more complex.

Reflecting these results back to the drone operation; lower η values can be reached by effective quarantine measures and a way to reach that is to use remote testing operations such that the possibility of spreading the disease in any hospital or testing environment is reduced due to lower number of people outside and as a consequence less dense hospitals. A flattened curve also means medical resources can be used more efficiently and more people can be treated in a successful, more attentive way. By this way a county can overcome an epidemic/ pandemic situation with minimal damage to its’ medical capacity and economy; therefore, minimal damage to its’ citizens and inhabitants.

Second Scenario: Varying Initial Conditions for Evaluating the Effectiveness of the Operation

Figures above show the realizations for different initial conditions where the initial infected population is varied as 10, 20, 50 and 100. The η values are 0.2 for left and 0.4 for right figure.

For η = 0.4, it is clear that the peak of the curve shifts towards the origin while keeping the width almost same. This is as expected, because more infected people in the beginning would cause more people to be infected in a shorter time and as the intervention factor η is constant for all curves the peak value and trend doesn’t change. However, again as mentioned above, higher I(0) also causes the overshoot to happen in a closer date; so, health system failure and related costs are amplified in reality which is not displayed in the graphs. This commentary on the right figure is also similarly applicable to higher η values thus, they are not displayed here.

For η = 0.2, the damping is still valid in general, hence the overshoot doesn’t happen in this realization for I(0) = 10, 20 and 50. When I(0) is 100, it can be seen that an overshoot occurs and to not exceed this limit higher intervention measures need to be taken. In theory lower η values would compensate this difference; yet in practice this doesn’t seem achievable unless lockdowns and similar higher authority intervention measures are taken. As those higher intervention measures are also applicable to any other realization that can be made, and it is not in the scope of this proposed strategy they are not treated. So, the conclusion is that for high I(0) values this operation alone is not adequate but can be used to improve the taken measures.

Third Scenario: Varying T/N for Evaluating the Impact of More Tests

Last scenario to be evaluated is the impact of increased number of tests as the drone operation intends to increase the number of daily tests as well by providing a logistic solution. The figure above shows 10, 100 and 1000 thousand times more tests being performed for η = 0.6 and I(0) = 8. The result is that more tests shifts the peak to a further date, but the peak value and width of the curve is also increased. An explanation would be that more tests result in more validated cases, so both the peak and width increase with the test number. Shifted peak and increased is related to the effectiveness of intervention as more cases can be identified and quickly quarantined. In short, Q(t) increases as I(t) decreases. The increased peak value and width is related to the interpretation of the used model. The rate of being quarantined is proportional to the number of tests and quarantined individuals are transferred to the H(t) compartment according to the model, so peak value and width increases with tests as well. These trends are likewise for different η values, so they are not presented here. As a summary, though some extent of the relation is covered by the model we believe that the relation between test number and hospitalization is not reflected in depth detail.

Also, it must be noted that increasing the test number is essential to understand the dynamics of a disease, understanding the dynamics helps to better understand what measures are needed to be taken; so, the outbreak can be controlled. If one doesn’t test anyone then the official number of infected individuals would be 0.

Planning

Week 3: Make plan - research algorithm and model

Week 4: Research algorithm and drone - create model

Week 5: Implement algorithm - research drone

Week 6: Simulate algorithm - research drone

Week 7: Create presentation

Week 8: Give presentation

Milestones

Week 3: New subject chosen - plan made

Week 4: Research of algorithm done - model done

Week 5: Algorithm implemented and tested - drone research done

Week 6: Case example simulated - drone component list done

Week 7: Wiki finalized

Week 8: Presentation finalized

Task Division

Main Contribution

Efe Utku:

-Organizing and Structuring the Wikipage

-Written Problem Statement, Subject, Pre-Testing Phase, Testing Phase (How Sampling is Performed), Population Dynamics

-Performed/ Reported MATLAB Simulation

-Research and Briefing on all related subjects (27 listed reference)

Roel den Hoet - Research of algorithms, implementation and testing of algorithms, work on wiki page

Venislav Varbanov - Research, implementation, testing and description of algorithms

Weekly Contribution

The subject of the project and the structure of the group have changed in the third week; so, first three weeks are not included below.

---

17- 23/02/2020

Efe:

-Researched History of Epidemics/ Pandemics and their effect on societies [5 hours]

-Planned experimentation and modelling of population dynamics [5- 7 hours]

-Briefed the group about the new subject and drone operation idea [1 hour]

---

24- 01/02- 03/2020

Efe:

-Researched currently used intervention strategies and their impact, epidemic modelling, case studies [8 hours]

-Started simulating different epidemiological models for choosing the appropriate model (MATLAB) [10 hours]

---

02- 08/03/2020

Efe:

-Written Problem Statement, Subject [2 hours]

-Updated/ Finalized the WikiPage Template [0.5 hour]

-Researched Epidemic Modeling and Adjusting the Model [8 hours]

-Worked on MATLAB Simulation for Pop. Dynamics [5 hours]

Roel:

- Researched algorithms

- Updated the wiki page on User, Society and Enterprise

Venislav:

- Worked on simulating the spread of disease

---

09- 15/03/2020

Efe:

-Written Drone Ops., Pop. Dynamics Model [3 hours]

-Researched on test conducting, predictive methods for region/ people selection, existing datasets on epidemics [10 hours]

-Worked on MATLAB Simulation for Pop. Dynamics [5 hours]

Roel:

-Worked on Wiki page for Description of the Operation

Venislav:

- Worked on simulating the work of the drones

---

16- 22/03/2020

Efe:

-Updated Testing Phase, Problem Statement, Mathematical Model [3 hours]

-Researched on test conducting, intervention policies, effects of outbreaks, SEIQHR Model [8 hours]

-Worked on MATLAB Simulation for Pop. Dynamics [10 hours]

Roel:

- Updated Operation Description

- Researched Drones (State of the Art)

- Wrote drone section on Wiki

---

24- 30/03/2020

Efe:

-Researched/ written Pre-Test Phase (How Sampling is Performed and Operation Bases) [4.5 hours]

- Constructed Flow Diagram of the model, adjusted the equations for Wikipage [0.5 hours]

- Performed MATLAB Simulation and reported results

Roel:

- Rewrote User section of the wiki

- Updated drone section

---

References

Academic

Al-Tawfiq, J. A., & Memish, Z. A. (2020). Diagnosis of SARS-CoV-2 Infection based on CT scan vs. RT-PCR: Reflecting on Experience from MERS-CoV. Journal of Hospital Infection. doi: 10.1016/j.jhin.2020.03.001

Chowell, G., Castillo-Chavez, C., Fenimore, P. W., Kribs-Zaleta, C. M., Arriola, L., & Hyman, J. M. (2004). Model Parameters and Outbreak Control for SARS. Emerging Infectious Diseases, 10(7), 1258–1263. doi: 10.3201/eid1007.030647

Chowell, D., Safan, M., & Castillo-Chavez, C. (2016). Modeling the Case of Early Detection of Ebola Virus Disease. Mathematical and Statistical Modeling for Emerging and Re-Emerging Infectious Diseases, 57–70. doi: 10.1007/978-3-319-40413-4_5

Dietz, K., & Heesterbeek, J. A. P. (2000). Bernoulli was ahead of modern epidemiology. Nature, 408(6812), 513–514. doi: 10.1038/35046270

Donnelly, C. A., Ghani, A. C., Leung, G. M., Hedley, A. J., Fraser, C., Riley, S., … Anderson, R. M. (2003). Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong. The Lancet, 361(9371), 1761–1766. doi: 10.1016/s0140-6736(03)13410-1

Gakwaya, N. J., & Priya, S. M. (2019). Contagious Diseases Prediction in Healthcare Over Big Data. Lecture Notes on Data Engineering and Communications Technologies Proceeding of the International Conference on Computer Networks, Big Data and IoT (ICCBI - 2018), 127–132. doi: 10.1007/978-3-030-24643-3_14

Hui, D. S.-C., Wong, P.-C., & Wang, C. (2003). SARS: clinical features and diagnosis. Respirology, 8(s1). doi: 10.1046/j.1440-1843.2003.00520.x

Ibrahim, N., Akhir, N. S. M., & Hassan, F. H. (2017). Predictive analysis effectiveness in determining the epidemic disease infected area. doi: 10.1063/1.5005397

Jackson, M. L., Nguyen, M., Kirlin, B., & Madziwa, L. (2015). Self-Collected Nasal Swabs for Respiratory Virus Surveillance: Table 1. Open Forum Infectious Diseases, 2(4). doi: 10.1093/ofid/ofv152

Katriel, G. (2013). Stochastic Discrete-Time Age-Of-Infection Epidemic Models. International Journal of Biomathematics, 06(01), 1250066. doi: 10.1142/s1793524512500660

Kermack, W. O., & McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 115(772), 700–721. doi: 10.1098/rspa.1927.0118

Leung, G. M., Hedley, A. J., Ho, L.-M., Chau, P., Wong, I. O., Thach, T. Q., … Lam, T.-H. (2004). The Epidemiology of Severe Acute Respiratory Syndrome in the 2003 Hong Kong Epidemic: An Analysis of All 1755 Patients. Annals of Internal Medicine, 141(9), 662. doi: 10.7326/0003-4819-141-9-200411020-00006

Mossong, J., Hens, N., Jit, M., Beutels, P., Auranen, K., Mikolajczyk, R., … Edmunds, W. J. (2008). Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases. PLoS Medicine, 5(3). doi: 10.1371/journal.pmed.0050074

Safi, M. A., & Gumel, A. B. (2010). Global asymptotic dynamics of a model for quarantine and isolation. Discrete & Continuous Dynamical Systems - B, 14(1), 209–231. doi: 10.3934/dcdsb.2010.14.209

Smolinski, M. S., Hamburg, M. A., & Lederberg, J. (2003). Microbial threats to health: emergence, detection, and response:Washington, DC: National Academies Press.

Tulchinsky, T. H., & Varavikova, E. A. (2014). Communicable Diseases. The New Public Health, 149–236. doi: 10.1016/b978-0-12-415766-8.00004-5

Yaari, R., Katriel, G., Stone, L., Mendelson, E., Mandelboim, M., & Huppert, A. (2016). Model-based reconstruction of an epidemic using multiple datasets: understanding influenza A/H1N1 pandemic dynamics in Israel. Journal of The Royal Society Interface, 13(116), 20160099. doi: 10.1098/rsif.2016.0099

Website

CID Associates, Inc. (n.d.). Modular Laboratories. Retrieved from https://www.cidbuildings.com/modular-laboratories.html

Clinical Specimens: Novel Coronavirus (2019-nCoV). (2020, March 25). Retrieved from https://www.cdc.gov/coronavirus/2019-nCoV/lab/guidelines-clinical-specimens.html

Current information about the novel coronavirus (COVID-19). (n.d.). Retrieved from https://www.rivm.nl/en/news/current-information-about-novel-coronavirus-covid-19

Fisher Scientific. (n.d.). Retrieved from https://www.fishersci.nl/nl/en/promotions/applied-biosystems-stepone-steponeplus-real-time-pcr-systems.html

Health equipment - Hospital beds - OECD Data. (n.d.). Retrieved from https://data.oecd.org/healtheqt/hospital-beds.htm

Laboratories. (n.d.). Retrieved from https://www.portafab.com/laboratories.html

Modular Laboratories & Specialty Portable Buildings. (n.d.). Retrieved from https://vanguardmodular.com/specialty/modular-laboratories/

Modular, Portable Labs & Prefabricated Buildings. (n.d.). Retrieved from https://www.starrco.com/modular-clean-rooms/modular-labs/

(n.d.). Retrieved from https://worldpopulationreview.com/countries/netherlands-population/cities/

Netherlands Birth Rate 1950-2020. (n.d.). Retrieved from https://www.macrotrends.net/countries/NLD/netherlands/birth-rate

Netherlands Death Rate 1950-2020. (n.d.). Retrieved from https://www.macrotrends.net/countries/NLD/netherlands/death-rate

Netherlands now home to 6,412 coronavirus patients, up 15%; 80 more patients died. (2020, March 25). Retrieved from https://nltimes.nl/2020/03/25/netherlands-now-home-6412-coronavirus-patients-15-80-patients-died

QuantStudio 12K Flex Real-Time PCR System. (n.d.). Retrieved from https://www.thermofisher.com/de/de/home/life-science/pcr/real-time-pcr/real-time-pcr-instruments/quantstudio-12k-flex-real-time-pcr-system.html

StepOnePlus™ StepOnePlus™ Real-Time PCR System Upgrade - Products Home. (n.d.). Retrieved from https://www.fishersci.fi/shop/products/steponeplus-real-time-pcr-system-upgrade-2/15351295

Use of laboratory methods for SARS diagnosis. (2015, July 24). Retrieved from https://www.who.int/csr/sars/labmethods/en/

Wappes, J. (2020, January 24). Studies highlight nCoV similarity with SARS, family transmission. Retrieved from http://www.cidrap.umn.edu/news-perspective/2020/01/studies-highlight-ncov-similarity-sars-family-transmission