Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage

Abstract

We extend the classical SIRS epidemic model incorporating media coverage from a deterministic framework to a stochastic differential equation (SDE) and focus on how environmental fluctuations of the contact coefficient affect the extinction of the disease. We give the conditions of existence of unique positive solution and the stochastic extinction of the SDE model and discuss the exponentialp-stability and global stability of the SDE model. One of the most interesting findings is that if the intensity of noise is large, then the disease is prone to extinction, which can provide us with some useful control strategies to regulate disease dynamics.

Effect of Awareness Programs on the Epidemic Outbreaks with Time Delay

“…Liu et al took into the random perturbation [36]. In [37], the authors extended the classical SIRS epidemic model from a deterministic framework to a stochastic differential equation, and then they gave the conditions of existence of unique positive solution and the stochastic extinction and discussed the exponential p-stability and global stability.…”

Dynamics Analysis of a Stochastic SIR Epidemic Model

“…Most natural phenomena do not follow strictly deterministic laws but rather oscillate randomly about some average values, so that the population density never attains a fixed value with the advancement of time [20,21]. Recent advances in stochastic differential equations enable a lot of authors to introduce randomness into deterministic model of physical phenomena to reveal the effect of environmental variability, whether it is a random noise in the system of differential equations or environmental fluctuations in parameters; see [12,13,[22][23][24][25][26][27][28][29][30]. Of them, Tuckwell and Williams [28] investigated the properties of a simple discrete time stochastic epidemic model.…”

Cholera model incorporating media coverage with multiple delays

“…Theorem 3. When R 0 > 1, the model system (15)(16)(17)(18)(19) has an only endemic equilibrium, which is locally asymptotically stable if and only if the aforementioned condition (26) is satisfied.…”