Dynamic Behavior of a Stochastic Tungiasis Model for Public Health Education

Abstract

In this paper, we study the dynamic behavior of a stochastic tungiasis model for public health education. First, the existence and uniqueness of global positive solution of stochastic models are proved. Secondly, by constructing Lyapunov function and using It o ^ formula, sufficient conditions for disease extinction and persistence in the stochastic model are proved. Thirdly, under the condition of disease persistence, the existence and uniqueness of an ergodic stationary distribution of the model is obtained. Finally, the importance of public health education in preventing the spread of tungiasis is illustrated through the combination of theoretical results and numerical simulation.

Dynamic Analysis of a Stochastic Delayed SEIRS Epidemic Model with Lévy Jumps and the Impact of Public Health Education

“…Assume that the total number of the population is 800, and the initial value is (S(0), E(0), I(0), R(0)) = (300,200,125,175). Parameter values are derived from references [5,[34][35][36][37] and are presented in Table 1.…”

Dynamic Behavior of a Stochastic Avian Influenza Model with Two Strains of Zoonotic Virus

“…Of course, our work should be further expanded. According to Reference [18], the first possible extension is that the parameters of the model are independent of each other, and different stochastic processes can be used to describe their dynamics. Obtaining or estimating parameters from the cases of infectious diseases that have occurred, as well as conducting numerical simulation studies through existing models so as to discuss the differences in the results obtained, is another direction for our next efforts.…”

“…Therefore, the important factor of environmental noise must be considered when establishing the corresponding mathematical model of infectious diseases. Compared with the deterministic infectious disease model, the discussion of the stochastic model is more in line with the law of disease transmission [13][14][15][16][17][18]. Inspired by [19][20][21][22][23], we assume that the random perturbation under the influence of white noise is proportional to the variables S a , E a , I a , S h , I h , and R h in the model (1) to obtain a stochastic model…”