A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching

Abstract

In this paper, we propose and discuss a stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching. First of all, we show that there is a unique positive solution, which is a prerequisite for analyzing the long-term behavior of the stochastic model. Then, a threshold dynamic determined by the basic reproduction number R s 0 is established: the disease can be eradicated almost surely if R s 0 < 1 and under mild extra conditions, whereas if R s 0 > 1 , the densities of the distributions of the solution can converge in L 1 to an invariant density by using the Markov semigroups theory. Finally, based on realistic parameters obtained from previous literatures, numerical simulations have been performed to verify our analytical results.

National Holidays and Social Mobility Behaviors: Alternatives for Forecasting COVID-19 Deaths in Brazil

“…The Susceptible–Exposed–Infected–Recovered–Dead model, also known as SEIRD [ 24 , 25 ], is an epidemiological analysis based on the Susceptible–Infected–Removed model, known as SIR [ 26 , 27 ]. SEIRD is intended to enhance the SIR model in order to explain the evolution of a population in terms of transmissibility, contact rates, and the expected duration of infection in the course of an outbreak.…”

Threshold dynamics for a class of stochastic SIRS epidemic models with nonlinear incidence and Markovian switching

“…Other environmental noise can be introduced in the epidemics models named color noise or telegraph noise [15,18,29] and can be illustrated like a switching between two or more regimes of environment which change through factors such as socio-cultural factors, changes in climate and nutrition. Often the switching among different environments is memoryless and the waiting time for the next switching follows an exponential distribution [2,39].…”

“…, N }. In [19] Lan et al explored the dynamics of a stochastic SIRS epidemic model with non-monotone incidence rate and Markovian switching. They addressed the threshold value of the disease that determines persistence and extinction of the disease and using the Markov semigroups theory they proved that the densities of the distributions of the solution can converge in L 1 to an invariant density.…”

Positive Recurrence and Extinction of Hybrid Stochastic SIRS Model with Nonlinear Incidence Rate

“…Some scholars have studied the effect of Le � vy noise on epidemic models [20,21]. Although many scholars have studied the different properties of epidemic models with white noise and Markovian switching [22][23][24][25][26], there are few studies on the positive recurrence and extinction of SIRS models with the abovementioned general incidence rate. In this paper, we will study the abovementioned properties of stochastic hybrid SIRS model with the following form:…”