Threshold dynamics of reaction-diffusion partial differential equations model of Ebola virus disease

作     者：Kazuo Yamazaki 

作者机构：University of Rochester Department of Mathematics Rochester NY 14627 USA 

出 版 物：《International Journal of Biomathematics》 (生物数学学报（英文版）)

年 卷 期：2018年第11卷第8期

页      面：235-264页

核心收录：

学科分类：0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Basic reproduction number Ebola persistence stability 

摘      要：We study the reaction-diffusion Ebola PDE model that consists of equations that govern the evolution of susceptible, in fee ted, recovered and deceased human individuals, as well as Ebola virus pathogens in the environment, with diffusive terms in all except the equation of the deceased human individuals. Under the setting of a spatial domain that is bounded, we prove the global well-posedness of the system;in contrast to the previous work on similar models such as cholera, avian influenza, malaria and dengue fever, diffusion coefficients may be different. Moreover, we derive its basic reproduction number, and under the condition that the diffusion coefficients of the susceptible and infected hosts are same, we prove the global stability of the disease-free-equilibrium, and uniform persistence in cases when the basic reproduction number lies beneath and above one, respectively. Again, we do not require that the diffusion coefficients of the recovered hosts be the same as the diffusion coefficients of the susceptible and infected hosts, in contrast to previous work on other models of infectious diseases. Another technical difficulty in our model is that the solution semiflow is not compact due to the lack of diffusion in the equation of the deceased human individuals;we overcome this difficulty using functional analysis techniques concerning Kura to wski measure of non-compactness.