#### Event Title

An Application of Compartmental Infectious Disease Modeling

#### Session Number

Project ID: MATH 1

#### Advisor(s)

Dr. Patrick Davis; Illinois Mathematics and Science Academy

#### Discipline

Mathematics

#### Start Date

22-4-2020 9:45 AM

#### End Date

22-4-2020 10:00 AM

#### Abstract

Compartmental modeling of infectious disease allows researchers to analyze the spread of a pathogen through a population and can contribute to determining optimal control strategies. Using this framework, we modelled the spread of influenza through a closed population of students, as motivated by the 2018 “Flu-pocalypse” that occured at IMSA. The students were sorted into susceptible, exposed, infectious, symptomatic, and recovered compartments of the disease. By utilizing differential equations, we model the flow at which the members of the population exit their respective compartments and transition into the next. These differential equations include several parameters which account for various behaviors of the population members and characteristics of the disease. Using these differential equations, we construct the corresponding Jacobian matrix to systematically determine the value of R0, the basic reproduction number of our model. R0is defined as the average number of new cases of an infection caused by one typical infected individual in a population consisting of only susceptibles; it is calculated by evaluating the dominant eigenvalue of the next-generational matrix of the infected subsystem. If R0>1, an epidemic will occur; and if R0<1, then it will not. In addition to simulating the disease, we proved the existence/uniqueness and non-negativity of a solution to our model given appropriate initial conditions.

An Application of Compartmental Infectious Disease Modeling

Compartmental modeling of infectious disease allows researchers to analyze the spread of a pathogen through a population and can contribute to determining optimal control strategies. Using this framework, we modelled the spread of influenza through a closed population of students, as motivated by the 2018 “Flu-pocalypse” that occured at IMSA. The students were sorted into susceptible, exposed, infectious, symptomatic, and recovered compartments of the disease. By utilizing differential equations, we model the flow at which the members of the population exit their respective compartments and transition into the next. These differential equations include several parameters which account for various behaviors of the population members and characteristics of the disease. Using these differential equations, we construct the corresponding Jacobian matrix to systematically determine the value of R0, the basic reproduction number of our model. R0is defined as the average number of new cases of an infection caused by one typical infected individual in a population consisting of only susceptibles; it is calculated by evaluating the dominant eigenvalue of the next-generational matrix of the infected subsystem. If R0>1, an epidemic will occur; and if R0<1, then it will not. In addition to simulating the disease, we proved the existence/uniqueness and non-negativity of a solution to our model given appropriate initial conditions.