Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence

This paper investigates the dynamics of a COVID-19 stochastic model with isolation strategy. The white noise as well as the Levy jump perturbations are incorporated in all compartments of the suggested model. First, the existence and uniqueness of a global positive solution are proven. Next, the stochastic dynamic properties of the stochastic solution around the deterministic model equilibria are investigated. Finally, the theoretical results are reinforced by some numerical simulations.

Mathematical analysis and simulation of a stochastic COVID-19 Lévy jump model with isolation strategy.

In this paper, a stochastic epidemic model with logistic growth and saturated treatment is formulated to probe the effect of white noise on population. We show that the proposed autonomous stochastic model possess a unique and non-negative solution. We obtain the sufficient conditions for extinction of the infectious disease and persistent in the mean of the stochastic autonomous epidemic model with probability one. That is, if ℛ 0 ˜ 1 , under some parametric conditions then the infection goes to extinction with probability one and if ℛ 0 ˜ > 1 , under some parametric conditions then the infection persist with probability one. By using Has’minskii’s theory of periodic solutions, we show that the stochastic non-autonomous epidemic model has at least one nontrivial positive θ -periodic solution. Finally, the theoretical results are illustrated by numerical simulations which obtains some additional interesting phenomena.

Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment

In this discourse, we establish and investigate the pervasive of environmental variability in a deterministic epidemic model with saturated incidence rate and saturated treatment function. We exemplify that the proposed stochastic model reveals an exclusive and universal positive solution. We deal with equilibrium solution of stochastic model which contribute few biological intrinsic manifestation for the model. We attain the sufficient conditions for extinction of the infectious disease and persistent in the mean of the stochastic epidemic model with probability one, if ℛ 0 ˜ 1 and if ℛ 0 ˜ > 1 respectively. Eventually, numerical probing is furnished to elucidate the analytical outcomes.

Dynamic threshold probe of stochastic SIR model with saturated incidence rate and saturated treatment function

A stochastically perturbed SIRS epidemic model with two viruses is formulated to investigate the effect of intensities of white noise on each population. We prove that the stochastic model has a non-negative solution that belongs to a positively invariant set. By applying a novel combination of suitable Lyapunov functions, we obtain that the asymptotic behaviour of the stochastic model holds a disease-free equilibrium if R 0 ≤ 1 and investigate pth-moment exponential stability. Then we derive the sufficient conditions for the solution of the stochastic model that fluctuates around the endemic equilibrium if R 0 > 1 . Furthermore, the suitable conditions for the extinction and persistence of the diseases are established due to intensities of white noise in large. Finally, the theoretical results are illustrated by numerical investigations.

Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses

We consider a stochastically perturbed Nowak-May model of virus dynamics within a host. We prove the global existence of unique strong solution. Using the Lyapunov method, we found sufficient conditions for the stochastic asymptotic stability of equilibrium solutions of this model.

Stochastic Asymptotic Stability of Nowak-May Model with Variable Diffusion Rates

In this paper, we explore the stochastic viral infection model with immune impairment and show that this model has a unique global solution. Using the Lyapunov method, we investigate the stochastic stability of equilibrium solutions of this model. Finally, sufficient condition for persistence of the disease is established and illustrate our mathematical findings.

Analysis of Stochastic Viral Infection Model with Immune Impairment

In this paper, we explore the stochastic viral infection model and show that this model has a unique global solution. We use the method of Lyapunov function to study the stochastic asymptotic stabi...

Analysis of stochastic viral infection model with lytic and nonlytic immune responses

This article presents a SIRS epidemic model with stochastic effect. For the stochastic version, we prove the existence and uniqueness of the solution of this stochastic SIRS model. In addition, sufficient conditions for the stochastic stability of equilibrium solutions are provided. Finally, numerical visualization is presented to justify our results.

R. Rajaji

Papers

Stochastic Asymptotic Stability of Nowak-May Model with Variable Diffusion Rates

Analysis of Stochastic Viral Infection Model with Immune Impairment

Analysis of stochastic viral infection model with lytic and nonlytic immune responses

Dynamics of Stochastic SIRS Model