### Mathematical Biosciences and Engineering

2015, Issue 1: 135-161. doi: 10.3934/mbe.2015.12.135

# Analysis of SI models with multiple interacting populations using subpopulations

• Received: 01 January 2014 Accepted: 29 June 2018 Published: 01 December 2014
• MSC : Primary: 92D30; Secondary: 37C75.

• 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 theinteractions 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.

Citation: Evelyn K. Thomas, Katharine F. Gurski, Kathleen A. Hoffman. Analysis of SI models with multiple interacting populations using subpopulations[J]. Mathematical Biosciences and Engineering, 2015, 12(1): 135-161. doi: 10.3934/mbe.2015.12.135

### Related Papers:

• 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 theinteractions 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.

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