Vector-borne diseases models with residence times – A Lagrangian perspective

Derdei Bichara, Carlos Castillo-Chavez

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)128-138
Number of pages11
JournalMathematical Biosciences
Volume281
DOIs
StatePublished - Nov 1 2016

Fingerprint

Disease Vectors
vector-borne diseases
Residence Time
disease models
Basic Reproduction Number
Patch
Basic Reproduction number
Globally Asymptotically Stable
disease prevalence
Nonlinear Dynamics
Endemic Equilibrium
Interaction
Infection
Interior
Model
infection
Numerical Simulation
Configuration
Computer simulation
Modeling

Keywords

  • Basic reproduction number
  • Global stability
  • Human dispersal
  • Nonlinear dynamical systems
  • Vector-borne diseases

ASJC Scopus subject areas

  • Statistics and Probability
  • Medicine(all)
  • Modeling and Simulation
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Cite this

Vector-borne diseases models with residence times – A Lagrangian perspective. / Bichara, Derdei; Castillo-Chavez, Carlos.

In: Mathematical Biosciences, Vol. 281, 01.11.2016, p. 128-138.

Research output: Contribution to journalArticle

@article{865a0f0175a8444ea2a9a050edd66a7e,
title = "Vector-borne diseases models with residence times – A Lagrangian perspective",
abstract = "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.",
keywords = "Basic reproduction number, Global stability, Human dispersal, Nonlinear dynamical systems, Vector-borne diseases",
author = "Derdei Bichara and Carlos Castillo-Chavez",
year = "2016",
month = "11",
day = "1",
doi = "10.1016/j.mbs.2016.09.006",
language = "English (US)",
volume = "281",
pages = "128--138",
journal = "Mathematical Biosciences",
issn = "0025-5564",
publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Vector-borne diseases models with residence times – A Lagrangian perspective

AU - Bichara, Derdei

AU - Castillo-Chavez, Carlos

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

UR - http://www.scopus.com/inward/record.url?scp=84988967222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988967222&partnerID=8YFLogxK

U2 - 10.1016/j.mbs.2016.09.006

DO - 10.1016/j.mbs.2016.09.006

M3 - Article

VL - 281

SP - 128

EP - 138

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

ER -