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Control Strategies in Multigroup Models: The Case of the Star Network Topology

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Abstract

In this paper, we propose control strategies for multigroup epidemic models. We use compartmental \({\textit{SIRS}}\) models to study the dynamics of n host groups sharing the same source of infection in addition to the transmission among members of the same group. In particular, we consider a model for infectious diseases with free-living pathogens in the environment and a metapopulation model with a central patch. We give the detailed derivation of the target reproduction number under three public health interventions and provide the corresponding biological insights. Moreover, using the next-generation approach, we calculate the basic reproduction numbers associated with subsystems of our models and determine algebraic connections to the target reproduction number of the complete model. The analysis presented here illustrates that understanding the topological structure of the infection process and partitioning it into simple cycles is useful to design and evaluate the control strategies.

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Acknowledgements

The authors acknowledge suggestions from an anonymous editor and a referee that helped to improve the quality of the manuscript.

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Authors and Affiliations

  1. Centro de Investigación en Matemáticas, Apartado Postal 402, C.P. 36240, Guanajuato, Mexico

    Fernando Saldaña & Ignacio Barradas

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  1. Fernando Saldaña
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  2. Ignacio Barradas
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Correspondence to Fernando Saldaña.

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Saldaña, F., Barradas, I. Control Strategies in Multigroup Models: The Case of the Star Network Topology. Bull Math Biol 80, 2978–3001 (2018). https://doi.org/10.1007/s11538-018-0503-6

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  • DOI: https://doi.org/10.1007/s11538-018-0503-6

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