This paper concentrates on the dynamics of a waterborne pathogen periodic PDE model with environmental pollution.For this model,we derive the basic reproduction number R0and establish a threshold type result on its gl...This paper concentrates on the dynamics of a waterborne pathogen periodic PDE model with environmental pollution.For this model,we derive the basic reproduction number R0and establish a threshold type result on its global dynamics in terms of R0,which predicts the extinction or persistence of diseases.More precisely,the disease-free steady state is globally attractive if R_(0)<1,while the system admits at least one positive periodic solution and the disease is uniformly persistent if R_(0)>1.Moreover,we carry out some numerical simulations to illustrate the long-term behaviors of solutions and explore the influence of environmental pollution and seasonality on the spread of waterborne diseases.展开更多
The existence of mild solutions for non-autonomous evolution equations with nonlocal conditions in Banach space is studied in this article. We obtained the existence of at least one mild solution to the evolution equa...The existence of mild solutions for non-autonomous evolution equations with nonlocal conditions in Banach space is studied in this article. We obtained the existence of at least one mild solution to the evolution equations by using Krasnoselskii’s fixed point theorem as well as the theory of the evolution family. The interest of this paper is that any assumptions are not imposed on the nonlocal terms and Green’s functions and a new alternative method is applied to prove the existence of mild solutions. The results obtained in this paper may improve some related conclusions on this topic. An example is given as an application of the results.展开更多
In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differen...In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differential equation are obtained by Banach and Krasnoselakii fixed point theorems, and sufficient conditions for the existence and uniqueness of the solution are also developed. In addition, the Hyers-Ulam stability of the solution is considered. At last, an example is given to illustrate the main results.展开更多
基金supported by the NSFC(12161079)the XSTP(KC2023058)。
文摘This paper concentrates on the dynamics of a waterborne pathogen periodic PDE model with environmental pollution.For this model,we derive the basic reproduction number R0and establish a threshold type result on its global dynamics in terms of R0,which predicts the extinction or persistence of diseases.More precisely,the disease-free steady state is globally attractive if R_(0)<1,while the system admits at least one positive periodic solution and the disease is uniformly persistent if R_(0)>1.Moreover,we carry out some numerical simulations to illustrate the long-term behaviors of solutions and explore the influence of environmental pollution and seasonality on the spread of waterborne diseases.
文摘The existence of mild solutions for non-autonomous evolution equations with nonlocal conditions in Banach space is studied in this article. We obtained the existence of at least one mild solution to the evolution equations by using Krasnoselskii’s fixed point theorem as well as the theory of the evolution family. The interest of this paper is that any assumptions are not imposed on the nonlocal terms and Green’s functions and a new alternative method is applied to prove the existence of mild solutions. The results obtained in this paper may improve some related conclusions on this topic. An example is given as an application of the results.
文摘In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differential equation are obtained by Banach and Krasnoselakii fixed point theorems, and sufficient conditions for the existence and uniqueness of the solution are also developed. In addition, the Hyers-Ulam stability of the solution is considered. At last, an example is given to illustrate the main results.
