Abstract

We develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure contact rates that are used in the traditional multi-group epidemic models with heterogeneous mixing. We apply this approach to a general n-patch SIS model whose basic reproduction number R0 is computed as a function of a patch residence-time matrix P. Our analysis implies that the resulting n-patch SIS model has robust dynamics when patches are strongly connected: There is a unique globally stable endemic equilibrium when R0>1, while the disease-free equilibrium is globally stable when R0≤1. Our further analysis indicates that the dispersal behavior described by the residence-time matrix P has profound effects on the disease dynamics at the single patch level with consequences that proper dispersal behavior along with the local environmental risk can either promote or eliminate the endemic in particular patches. Our work highlights the impact of residence-time matrix if the patches are not strongly connected. Our framework can be generalized in other endemic and disease outbreak models. As an illustration, we apply our framework to a two-patch SIR single-outbreak epidemic model where the process of disease invasion is connected to the final epidemic size relationship. We also explore the impact of disease-prevalence-driven decision using a phenomenological modeling approach in order to contrast the role of constant versus state-dependent P on disease dynamics.

Original languageEnglish (US)
Pages (from-to)2004-2034
Number of pages31
JournalBulletin of Mathematical Biology
Volume77
Issue number11
DOIs
StatePublished - Nov 1 2015

Fingerprint

SIR Epidemic Model
SIR
Patch
residence time
Residence Time
dispersal behavior
environmental risk
matrix
Disease Outbreaks
SIS Model
P-matrix
Basic Reproduction Number
Epidemic Model
patch dynamics
disease prevalence
Endemic Diseases
Eliminate
Basic Reproduction number
Endemic Equilibrium
Invasion

Keywords

  • Adaptive behavior
  • Dispersal
  • Epidemiology
  • Final size relationship
  • Global stability
  • Residence times
  • SIS–SIR models

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Immunology
  • Mathematics(all)
  • Computational Theory and Mathematics
  • Neuroscience(all)
  • Pharmacology

Cite this

SIS and SIR Epidemic Models Under Virtual Dispersal. / Bichara, Derdei; Kang, Yun; Castillo-Chavez, Carlos; Horan, Richard; Perrings, Charles.

In: Bulletin of Mathematical Biology, Vol. 77, No. 11, 01.11.2015, p. 2004-2034.

Research output: Contribution to journalArticle

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