Multistability, Infection-Induced Bifurcations and Chaos in a Discrete Population Model with Treatment

The paper is devoted to analyzing the mechanisms of spread and prevention of epidemics, based on a discrete model that takes into account the infection spread because of contacts among infected and susceptible individuals, disease-induced mortality, and the factor of treatment. Pathways leading to the complete extinction, complete recovery, and nontrivial coexistence of susceptible and infected individuals are revealed by bifurcation analysis. Parametric conditions of nontrivial modes of coexistence in the form of equilibrium, discrete cycle, quasiperiodic closed invariant curve and chaos are found. An extended analysis on transformation scenarios of these regimes in dependence of the variation of the rate of the infection spread and the treatment intensity is performed. Phenomena of infection-induced chaos and its suppression by treatment are discussed.