Jack DeWeese Computer Systems Research Lab

Purpose  Originally intended to create my own simulation with easily modified variables  Halfway through the year, switched to a more professional virus simulation software as a base for my own  Time constraints limited this development  Moved to finding ideal percentage of mass vaccination

Expectations  Program will accept wide range of variables: Viruses: ○ Rate of infection ○ Length of incubation, infection Population: ○ Number of total people, people vaccinated ○ Age

Additions to Original Program  Hospitals Sick people have a chance of going to the hospital when sick Value of chance adjustable according to severity of disease  Vaccination Percentage of population immune  Iterative data output Produces collections of data with varying population sizes, number of people vaccinated

Program Description  Every day everyone goes to their assigned workplace (with the exception of those who stay home if they are sick and as a result “decide” to stay home)  At each time step, chance of infection is used to determine if nearby agents will become infected and those already infected die if they have reached the end of the virus’ time span

Program Description (cont.)  Hospitals are included to add more detail to the simulation Isolates some infected people and concentrates the virus  Vaccination is merely a simple random mass vaccination (trace vaccination requires more advanced coding than was possible in the allowed timeframe)

Program Description (cont.)  Based on the MASON software platform used as a generic base for agent-based models (Java)  Jill Dunham created SIS/SIR/SEIR Epidemic Demonstration  Built off this to add additional features and create output features for mathematical models

Program Sample Run Very simple test runs (40 people) Visual model used for debugging

Problems Encountered  Time available for work, late start  Processing power of computer  Output features somewhat manual

Procedure  Ran hundreds of iterations of the simulation for data collection  Iterated over the variables of population size (consistent map size  variable population density) and percentage of population vaccinated  Program compiled results into averages  Excel performed quadratic regression to create formulas for simulation results

 Gives the total number of deaths or number infected:  ‘x’ is the number of people vaccinated  ‘r v ’ is the percentage of deaths/infection from vaccination  ‘r(x)’ is the number of deaths/infection as a result of the virus Minimizing Deaths/Infection

Minimizing Deaths/Infection (cont.)  To minimize overall deaths/infection, take the derivative of ‘f(x)’ and set equal to zero:

Fitting ‘r(x)’ to the Data  Used a quadratic model regression to produce the coefficients in ‘r(x)’ for each population size:

Deaths vs. Vaccinated Population of 300

Minimizing Deaths/Infection (cont.)  Solving for ‘x’:

Generalizing ‘r(x)’ to Population Size ‘n’  After gathering the results of the ‘r(x)’ models for populations sizes 50 through 450 in increments of 50, used a quadratic regression on the coefficients of x 2 and x terms of ‘r(x)’

Generalizing ‘r(x)’ to Population Size ‘n’ (cont.) β 1 (n) = -2(10) -5 n n β 2 (n) = -5(10) -8 n 2 + 2(10)

Other Variables  Iterations used to produce the previous data and regression models included population size only  Variables that can be easily incremented to produce similar models are: Population density Set of variables for virus (e.g. duration of infection) Size of households, workplaces Number of hospitals

Results  Program can now be used to model not only a given set of variables, but also a range of variables to produce a model that is a function of any given set of variables

Results (cont.)  Ex: To find the ideal number of people to vaccinate in a population with population parameters size n and density ρ, and virus parameters v k

Next Steps  To take this program further would require a more automated process of performing the quadratic regression models normally done in Excel  A more user-friendly input is also needed without programming experience