A Lyapunov functional for a SIRI model with nonlinear incidence of infection and relapse

作者：Georgescu, Paul^*; Zhang, Hong

来源：Applied Mathematics and Computation, 2013, 219(16): 8496-8507.

DOI：10.1016/j.amc.2013.02.044

• Compartmental model
• Nonlinear incidence
• Relapse
• Global stability
• Lyapunov functional

We analyze the dynamics of a disease propagation model with relapse under the assumption that the incidence of infection is given in an abstract, possibly bi-nonlinear form. Sufficient conditions for the local stability of equilibria are obtained by means of Lyapunov's second method and it is shown that global stability can be attained under suitable monotonicity conditions. The persistence of the system is then investigated and it is established that the basic reproduction number R-0 is a threshold parameter for the stability of the system. Alternate Lyapunov functionals are also introduced, being observed that the originating functional template generalizes both quadratic and Volterra functionals.

• 出版日期2013-4-15
• 单位江苏大学