Persistence and extinction of species in a disease-induced ecological system under environmental stochasticity

Stochastic Analysis for the Dual Virus Parallel Transmission Model with Immunity Delay

In this article, the qualitative properties of a stochastic dual virus parallel transmission model with immunity delay are analyzed. First, we use Lyapunov theory to study the existence and uniqueness of the global positive solution of the proposed model. Second, the threshold values of the persistence and extinction of two viruses were obtained. Finally, the numerical simulation verifies the theoretical results. The results show that the immunity delay and the intensity of noise have important effects on the two diseases spreading in parallel.

Analysis of stochastic disease including predator-prey model with fear factor and Lévy jump

In this paper, we investigate the dynamical properties of a stochastic predator-prey model with a fear effect. We also introduce infectious disease factors into prey populations and distinguish prey populations into susceptible prey and infected prey populations. Then, we discuss the effect of Lévy noise on the population considering extreme environmental situations. First of all, we prove the existence of a unique global positive solution for this system. Second, we demonstrate the conditions for the extinction of three populations. Under the conditions that infectious diseases are effectively prevented, the conditions for the existence and extinction of susceptible prey populations and predator populations are explored. Third, the stochastic ultimate boundedness of system and the ergodic stationary distribution without Lévy noise are also demonstrated. Finally, we use numerical simulations to verify the conclusions obtained and summarize the work of the paper.