Vector-borne diseases models with residence times - A Lagrangian perspective.
A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts' dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R0is computed and shown to depend on the relative environmental risk of infection. The model is robust, that is, the disease free equilibrium is globally asymptotically stable (GAS) if R0≤1 and a unique interior endemic equilibrium is shown to exist that is GAS whenever R0>1 whenever the configuration of host-vector interactions is irreducible. The effects of patchiness and groupness, a measure of host-vector heterogeneous structure, on the basic reproduction number R0, are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence.
Department of Mathematics, California State University, Fullerton, United States; Center for Computational and Applied Mathematics, 800 N. State College Blvd, Fullerton, CA 92831, United States. Electronic address: dbichara@fullerton.edu.
Derdei
D
Bichara
Simon A. Levin Mathematical, Computational and Modeling Science Center, Arizona State University, Tempe, AZ 85287, United States. Electronic address: ccchavez@asu.edu.
Carlos
C
Castillo-Chavez
D000818:Animals; D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000635:transmission*; D004199:Disease Vectors; D058872:Epidemics; D006801:Humans; D017711:Nonlinear Dynamics; D011157:Population Dynamics
Basic reproduction number; Global stability; Human dispersal; Nonlinear dynamical systems; Vector-borne diseases