Threshold dynamics of an age–space structured brucellosis disease model with Neumann boundary condition

• Published in: Nonlinear analysis: real world applications Vol. 50; pp. 192 - 217
• Main Authors: Yang, Junyuan, Xu, Rui, Li, Jiaxu
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.12.2019; Elsevier BV
• Subjects: Age–space structured model; Animals; Boundary conditions; Brucellosis; Computer simulation; Global stability; Infectious diseases; Mathematical models; Parameter sensitivity; Sensitivity analysis; The basic reproduction number; Zoonoses; The basic reproduction number; Brucellosis; Age–space structured model; Global stability
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2019.04.013

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 R0 is defined by the spectral radius of R(x). The calculation method is novel and simple. It is shown that when R0<1 the infectious disease will die out; when R0>1 the disease will be prevalent. Parameter sensitivity analysis on the expression of R0 shows that certain parameters are more effective to impact the value of R0. 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. •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.