Dynamics analysis of stochastic epidemic models with standard incidence

Abstract

In this paper, two stochastic SIRS epidemic models with standard incidence were proposed and investigated. For the non-autonomous periodic model, the sufficient criteria for extinction of the disease are obtained firstly. Then we show that the stochastic system has at least one nontrivial positive T-periodic solution under some conditions. For the model that are both disturbed by the white noise and telephone noise, we construct a suitable Lyapunov functions to verify the existence of a unique ergodic stationary distribution. Meanwhile, the sufficient condition for the extinction of the disease is also established. Finally, examples are introduced to illustrate the theoretical analysis. MSC: 60H10; 65C30; 91B70

Dynamics analysis of a delayed virus model with two different transmission methods and treatments

“…Using mathematical models to help discover the mechanism of viral transmission to predict the development of infectious diseases has become the mainstream method for controlling and preventing infectious diseases [9][10][11][12]. Therefore, for over a century, lots of mathematical models have been established to explain the evolution of the free virus in a body, and mathematical analysis was implemented to explore the threshold associated with eradication and persistence of the virus; for example, [13][14][15][16] studied the global dynamic behavior of HIV models, [17][18][19][20][21][22][23][24] analysed the global dynamics of HBV models [25][26][27][28].…”

Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

“…In recent decades, mathematicians have tried to study the spread of infectious diseases. Many disease models have been introduced to understand and analyze epidemics [1][2][3][4][5][6]. The simplest and best-known one is the SIR (susceptible, infections, removed) model, where the total population is divided into three compartments: susceptible (S), infections (I), and removed (R).…”

Periodic Solution of a Neutral Delay Leslie Predator-Prey Model and the Effect of Random Perturbation on the Smith Growth Model

“…On the contrary, biological populations multiply and thrive in nature, which will inevitably be affected by various environmental noise, so it is important to consider the effects of random disturbances on population dynamics [21][22][23][24][25][26][27][28][29]. In [30], the asymptotic stability of a stochastic May mutualism system was studied.…”