Dynamics Of Two Reaction-diffusion Epidemic Models

In this paper,we consider the dynamical properties of two reaction-diffusion epi-demic models.By applying the comparison principle and semigroup theory,we de-termine the existence of equilibrium.Based on this,we give a definition of basic reproduction numberR₀of the model using some literature results and obtain the stability properties of equilibrium.The specific working process is as follows:Chapter 1,we briefly introduce the background and research significance of the combination of epidemic model and reaction diffusion equation in order to understand the necessity for its combination.It emphasizes the development status at home and abroad of epidemic reaction diffusion model and explains the research problem and the main content in this paper.Chapter 2,we focus on dynamics of a diffusive SIRS epidemic model with three-dimensional nonlinear incidence rate.By applying the comparison principle and semi-group theory,we determine the existence of equilibrium and the influence of basic reproduction numberR₀on system:the disease-free equilibrium₀is globally attrac-tive forR₀<1;the model is uniform persistence forR₀>1.Then we consider the global asymptotic stability of₀under constant coefficients.Furthermore,we use Lya-punov function method to obtain the global stability of^*for the standard incidence rate.At the same time,numerical simulation is used to support the conclusion.Chapter 3,we mainly study dynamics of a SEIR reaction diffusion model with two transmission pathways.By applying the comparison principle and semigroup theory,we determine the existence of equilibrium and the influence of basic reproduction num-berR₀on system:whenR₀?1,the disease-free equilibrium has global asymptotic stability;whenR₀>1,system is uniform persistence,and we obtain the global asymp-totic stability of epidemic equilibrium^*under constant coefficients by constructing Lyapunov function.In the numerical simulation,combined with the current COVID-19,we attempt to use this simple model to justify the introduction of diffusion and input in the early period of COVID-19.Compared with some western countries which did not take an attitude towards COVID-19,the numerical simulation also shows the positive effectiveness of our epidemic prevention measures.