Analysis of an SEIR model with Non-Constant Population

Analysis of an SEIR model with Non-Constant Populationby Kylar Byrd and Tess Tracy, with Dr. Sunil Giri and Dr. Swarup Ghosh. Mathematical modeling can be useful in helping us to understand disease dynamics. Epidemiological models consist of differential equations with variables and parameters defined to portray these dynamics. We will be presenting the mathematics involved in formulating and analyzing a model for a disease such as influenza. We will first explain a simple SIR model, and then we will introduce our model. We will be looking at an SEIR model that incorporates the use of an exposed class as well as parameters such as death and birth rate that result in a nonconstant population. Using the linearization procedure, we find the threshold value, reproduction number and explore the local stability of disease-free equilibrium under different cases of reproduction number