TY - JOUR
T1 - Vector-borne diseases models with residence times – A Lagrangian perspective
AU - Bichara, Derdei
AU - Castillo-Chavez, Carlos
N1 - Funding Information:
We are grateful to the handling editor and two anonymous reviewers for their helpful comments and suggestions which led to an improvement of this paper. C.C.C is supported in part by grant #1R01GM100471-01 from the National Institute of General Medical Sciences (NIGMS) at the National Institutes of Health. The contents of this manuscript are solely the responsibility of the authors and do not necessarily represent the official views of DHS or NIGMS. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/11/1
Y1 - 2016/11/1
N2 - 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 R0 is 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.
AB - 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 R0 is 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.
KW - Basic reproduction number
KW - Global stability
KW - Human dispersal
KW - Nonlinear dynamical systems
KW - Vector-borne diseases
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U2 - 10.1016/j.mbs.2016.09.006
DO - 10.1016/j.mbs.2016.09.006
M3 - Article
C2 - 27622812
AN - SCOPUS:84988967222
SN - 0025-5564
VL - 281
SP - 128
EP - 138
JO - Mathematical Biosciences
JF - Mathematical Biosciences
ER -