Dynamic Analysis Of A Stochastic SIQHVS Infectious Disease Model With Semi-markov Switching

Infectious diseases are diseases that are transmitted from person to population,animal to animal,and population to animal by various pathogens through contact,airborne transmission,food or waterborne infection.The transmission process of the disease is inevitably affected by a variety of external environmental factors,which may switch from one state to another.The semi-Markov process is a stochastic process that can describe the occurrence of a series of states at random time,and the introduction of the semi-Markov process.Therefore,considering the influence of external environment,isolation policy,vaccination,media coverage,isolation resources,on the transmission dynamics of infectious diseases,a stochastic SIQHVS model with semi-Markov switching is established.This paper introduces the infectious disease models,expounds the research background and research significance of the stochastic model with semi-Markov switching,and gives the relevant definitions,theorems and lemma used in this paper.In the first part,considering the influence of the external environment,this paper establishes a stochastic SIQHVS model with semi-Markov switching,proves the uniqueness of the existence of the global positive solution by using the Lyapunov analysis method,gives the threshold and sufficient conditions for determining disease extinction and persistence,analyzes the influence of environmental disturbance intensity on disease dynamics,and verifies the theoretical results through numerical simulation.In the second part,considering the influence of vaccination on disease dynamics,this paper establishes a stochastic SIQHVS model with semi-Markov switching and vaccination,gives the threshold and sufficient conditions for determining disease extinction and persistence,and obtains that vaccination is beneficial to disease extinction through analysis,and finally verifies the authenticity and validity of the conclusions through numerical simulation.In the third part,this paper further adds the influence of media coverage and isolation resources on disease dynamics,and establishes a SIQHVS model with the influence of isolation resources and media coverage.The threshold and sufficient conditions for determining disease extinction and persistence are given,and through theoretical analysis,it is concluded that media coverage and isolation resources are conducive to suppressing the outbreak of epidemic,and finally numerical simulation verifies the correctness of the conclusion.