Stability analysis for a delayed SIR model with a nonlinear incidence rate

Abstract

We develop an SIR vector-bone epidemic model incorporating incubation time delay and the nonlinear incidence rate, where the growth of susceptibles is governed by the logistic equation. The threshold parameter R 0 is used to determine whether the disease persists in the population. The model always has the trivial equilibrium and the disease-free equilibrium whereas admits the endemic equilibrium if R 0 exceeds one. The disease-free equilibrium is globally asymptotically stable if R 0 is less than one, while the system is persistent if R 0 is greater than one. Furthermore, by applying the time delay as a bifurcation parameter, the local stability of the endemic equilibrium is discussed and it loses stability and Hopf bifurcation occurs as the length of the time delay increases past τ 0 under certain conditions. An example is carried out to illustrate the main results.

Transmissibility of epidemic diseases caused by delay with local proportional fractional derivative

“…Zhang et al [7] generated significant results elaborating the influence of time delay on the stability and measures of synthetic drugs transmission. Liu et al [8] incorporated incubation time delay in the susceptible, infected, recovered vector, bone epidemic model and discussed its stability with the logistic population growth. Rifhat et al [9] designed a stochastic SIRV model and explained the effects of environmental noises on the disease transmission.…”