Dynamics of a deterministic and a stochastic epidemic model combined with two distinct transmission mechanisms and saturated incidence rate.

The study of dynamics of epidemics, especially, double epidemics, has got paramount importance in the present days, since various health risks, an individual is exposed to due to the increasing global warming are unavoidable and/or due to limited medical resources available to handle suddenly developed disease. In view of this, we consider a study of an epidemic model with a double hypothesis, namely, SIR and SIRS mechanisms. First, we prove the local asymptotic stability of equilibrium points followed by the global stability of the disease for equilibrium established through the Lyapunov function. Next, we show the existence, extinction and persistence results of the stochastic system. Finally, some numerical examples are presented to support the theoretical results established. • Epidemic model with double hypothesis combined with SIR and SIRS transmission mechanisms. • Global existence of a positive solution. • Global stability of the disease-free equilibrium. • Extinction of the diseases. [ABSTRACT FROM AUTHOR]