A Multi-patch Multi-group Vector-borne Disease Model With Lagrangian Approach

We develop a multi-group Lagrangian patch model to study the effects of human and mosquito movement and spatial heterogeneity on the spread of vector-borne diseases.The basic reproduction number of the model,?₀,is defined and the strong connectivity of host–vector network is directly characterized by the residence times matrices of humans and mosquitoes.In particular,we give the definition and characterization of the strong connectivity of the general infectious disease network,and apply them to the study of the global stability of the disease-free equilibrium.We show that the dynamic behavior of the model is completely determined by its basic reproduction number,that is,if?₀?1,then the disease-free equilibrium is globally asymptotically stable;if?₀>1,then there exists an endemic equilibrium which is globally asymptotically stable.Moreover,we obtain biologically meaningful upper and lower bounds on the basic reproduction number which are dependent or independent of the residence times matrices,and find that the upper bound is substantially different from that of the corresponding Eulerian patch model.In particular,the heterogeneous mixing of humans and mosquitoes in a homogeneous environment always increases the basic reproduction number.When only human movement between two patches is concerned,we show that the subdivision of hosts leads to a larger basic reproduction number.In addition,we numerically investigate the dependence of the basic reproduction number and the total number of infected hosts on the residence times matrix of humans,and compare the influence of different vector control measures on disease transmission.