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Mathematical Biosciences and Engineering (MBE)
 

Analysis of SI models with multiple interacting populations using subpopulations

Pages: 135 - 161, Volume 12, Issue 1, February 2015      doi:10.3934/mbe.2015.12.135

 
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Evelyn K. Thomas - Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250, United States (email)
Katharine F. Gurski - Department of Mathematics, Howard University, Washington, DC 20059, United States (email)
Kathleen A. Hoffman - Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250, United States (email)

Abstract: Computing endemic equilibria and basic reproductive numbers for systems of differential equations describing epidemiological systems with multiple connections between subpopulations is often algebraically intractable. We present an alternative method which deconstructs the larger system into smaller subsystems and captures the interactions between the smaller systems as external forces using an approximate model. We bound the basic reproductive numbers of the full system in terms of the basic reproductive numbers of the smaller systems and use the alternate model to provide approximations for the endemic equilibrium. In addition to creating algebraically tractable reproductive numbers and endemic equilibria, we can demonstrate the influence of the interactions between subpopulations on the basic reproductive number of the full system. The focus of this paper is to provide analytical tools to help guide public health decisions with limited intervention resources.

Keywords:  Reproductive number, stability, SI model, compartmental model, spread of HIV.
Mathematics Subject Classification:  Primary: 92D30; Secondary: 37C75.

Received: January 2014;      Accepted: November 2014;      Available Online: December 2014.

 References