The Asymptotic Behavior Of Fecal-oral Transmission Diseases Model On Evolving Domains

The fecal-oral transmission as a common way for infectious diseases to spread,has drawn public attention of many scholars.Because the virus can exist in the feces for several weeks,the fecal-oral transmission diseases are extremely easy to break out in a certain area,and there is a risk of disease within the family and close contacts,thus resulting in endemic diseases.At present,there is still a lack of effective drug symptomatic treatment.Therefore,it is very essential and necessary to study the propagation law and diffusion mechanism of the virus,so as to promote the prevention and treatment of endemic infectious diseases such as fecal-oral diseases.This paper is concerned with a reaction-diffusion system on evolving domains describing the dynamics of the model of the fecal-oral transmission diseases,and corresponding models of fecal-oral transmission diseases are established in the growing domain and the periodically evolving domain respectively.The stability of endemic and disease-free equilibrium points is proved by using the basic reproduction number as an index,and the important impacts of two domain evolution modes on the fecal-oral transmission diseases are revealed.This paper is mainly divided into the following three parts:In Chapter 1,we mainly introduce the research background and research status of the problem,including the relevant researches on the model of fecal-oral transmission diseases and the evolving domains,and generally expounds the main contents of the whole paper.In Chapter 2,we study the fecal-oral transmission diseases on a growing domain.We introduce the basic reproduction number by means of the eigenvalue problem and investigate the asymptotic behavior of solutions to the reaction-diffusion by giving the boundedness and the comparison principle of the solution.We use Lyapunov method to prove the stability of disease-free equilibrium point.The stability of endemic equilibrium is analyzed by constructing iterative sequences and applying the method of upper and lower solutions.Compared to the model counterpart with fixed domain,biological impacts of a growing domain on the spreading of infectious diseases are analyzed.In Chapter 3,we investigate the fecal-oral transmission diseases on a periodically evolving domain.The explicit expression of the basic reproduction number is given through spectral analysis and eigenvalue method.According to the means of upper and lower solutions and the construction of iterative sequences,the existence of T-periodic solutions when R0>1 and R0?1 are discussed respectively.Furthermore,we prove the stability of endemic and disease-free equilibrium point,and explore the relationship between domain evolution ratio and fecal-oral transmission diseases.