Threshold dynamics of an age–space structured brucellosis disease model with Neumann boundary condition. (December 2019) - Yang, Junyuan; Xu, Rui; Li, Jiaxu
Abstract: Brucellosis is a highly contagious zoonosis in the world caused by a group of bacteria from the genus brucella. It can infect both human and animals through eating contaminated food, breathing polluted air, and direct contact of the infected animals. The number of onset cases shows an increase tend in recent years, mainly in pastures and farms. To investigate the dynamics of brucellosis and capture the event of its spread, we propose a novel model that is an attempt for the first time ever to incorporate with both age-since-infection and spacial diffusion of the infection. We first analytically study the existence and uniqueness of the solution of the model, followed by positivity of the solutions. The location dependent reproduction number R ( x ) is explicitly calculated by a renewal process and the basic reproduction number R 0 is defined by the spectral radius of R ( x ) . The calculation method is novel and simple. It is shown that when R 0 < 1 the infectious disease will die out; when R 0 > 1 the disease will be prevalent. Parameter sensitivity analysis on the expression of R 0 shows that certain parameters are more effective to impact the value of R 0 . Based on this analysis and our intensive numerical simulations, we recommend that the herdsmen should make efforts to keep the living environment of their animals clean, and eliminate infectious animals timely. Highlights: We firstly propose a novel age–space structured brucellosis epidemic model. We calculate an explicit formulation for the next generator operator R ( x ) by the renewal equation. We give a general method to estimate the weighted coefficients for constructing Lyapunov functionals. We show some effectively control strategies for herdsman by uncertainty analysis.