A Study Of A Seasonal And Vaccinated Cellular Automata Infectious Disease Model

Infectious diseases threaten human health.It is of great significance to study seasonal and vaccinated infectious disease models.Cellular automata is a general modeling method consisting of a series of rules,which is different from the usual physical and functional models.It has a good effect in studying complex phenomena such as time,space and state discrete dynamics.There is a good analogy with the transmission mechanism of infectious diseases to overcome these drawbacks in the process of simulation,so a class of SIR infectious disease models with seasonal and vaccination based on two-dimensional cellular automata are studied in this paper.First of all,in the first chapter,the background and significance of the research topic are introduced.The main research contents and research trends in this field are analyzed at home and abroad.At the end of this chapter,the main research contents of this paper are introduced.Secondly,in the second chapter,we introduce the basic knowledge related to this paper,including some basic theories of cellular automata and the theory of local diffusion in mean field approximation theory.Finally,in the third chapter,based on the spread of infectious disease process,the population is divided into three categories: susceptible individuals(S),infected individuals(I),recovered individuals(R),an infectious disease model based on two-dimensional cellular automata is established and nonlinear discrete model based on mean-field approximation theory,mathematical analysis was carried out on the model.By calculating the spectral radius of the disease-free equilibrium Jacobian matrix,the local stability of the disease-free equilibrium is obtained and simulates infected person at the positive equilibrium with cellular neighbor structure of delta relationship.First,we consider two initial initialization States of model,which are the initial infected person is centered distributed and the initial infected person is randomly distributed,and investigate the influence of different initialization on the model.Second,consider the impact of different rates of vaccination on the speed of disease transmission.Third,the effects of different seasonal fluctuations in ? on the transmission of infectious diseases were considered.The model was calculated and simulated by software Matlab and Python.The following conclusions are obtained by numerical simulation:(1)When the initial patient of the disease is centered,the transmission speed of the infectious disease is less than the speed of transmission of the infectious disease when the initial patient is randomly distributed.(2)With the increase of the vaccination rate,the spread of infectious diseases will decrease,and the initial distribution of cellular automata will be more affected.(3)As the volatility increases,the number of affected people will also increase.