Anna Ghazaryan
Miami University, Ohio
Title
Regime dependent infection propagation fronts in a epidemiological model
Abstract
We consider a diffusive version of an S-I-S (Susceptible-Infected-Susceptible) epidemiological model which includes a saturating incidence in the size of the susceptible population. We seek traveling fronts in this model in the following regimes: when both susceptible and infected populations move around at comparable rates; when the infection slows the population down; when the infected population diffuses faster than the susceptible population. In all three regimes we show that traveling fronts exist. In the latter regime we derive a bound for the speeds of propagation of the infection. We also identify a regime when the spread of the disease is governed by the Burgers-FKPP equation. The paper uses applied dynamical system techniques and geometric singular perturbation theory. This is a joint work with Dr. Vahagn Manukian and two students, Jonathan Waldmanna and Priscilla Yinzime.