In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the...In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.展开更多
In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the ad...In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the advection and dilution terms,we transform the model to a reaction-difusion problem in a fixed domain.By means of eigenvalue problems,the threshold parameters are introduced.The asymptotic profiles of the solutions on an evolving domain are studied by using the threshold parameters and the upper and lower solutions method.The impact of the domain evolution rate on the persistence or extinction of species is analyzed.Numerical simulations are performed to illustrate our analytical results.展开更多
基金supported by the National Natural Science Foundation of China (No.12231008 and No.11971185)。
文摘In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.
基金This work was partially supported by the National Natural Science Foundation of China(11771381 and 11911540464).
文摘In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the advection and dilution terms,we transform the model to a reaction-difusion problem in a fixed domain.By means of eigenvalue problems,the threshold parameters are introduced.The asymptotic profiles of the solutions on an evolving domain are studied by using the threshold parameters and the upper and lower solutions method.The impact of the domain evolution rate on the persistence or extinction of species is analyzed.Numerical simulations are performed to illustrate our analytical results.
