SIS models and the impact of stress on infection rates.MI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

Abstract The impact of stress on the immunsystem has already been investigated in many studies. Similarly, many models of mathematical epidemiology have been created in recent decades. The goal of this talk is to combine both areas by including stress in a simple SIS model. Therefore, the first step is to gain insight into stress research and mathematical epidemiology. In particular, the R-value, bifurcations occurring in the process and their determination are of interest. Furthermore, we take a look at the well-known SIS model in which the population is divided into two groups - infected/infectious and susceptible. Descriptive parameters for this are the transmission rate and the recovery rate. Then we first incorporate the stress factor into both rates, under the simplified assumption that the population has a homogeneous stress level. In the subsequent model, we divide the population into different stress groups. We also study an SIS model with oscillating stress levels using a Poincaré map. In all these models we are interested in how stress affects infection rates. In our final model, we examine not only the effect of stress on infection counts, but also how infection counts affect stress levels. Of particular interest in the respective models is when an infectious disease remains endemic or declines.