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Characterization of differential susceptibility and differential infectivity epidemic models

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Abstract

Heterogeneity in susceptibility and infectivity is a central issue in epidemiology. Although the latter has received some attention recently, the former is often neglected in modeling of epidemic systems. Moreover, very few studies consider both of these heterogeneities. This paper is concerned with the characterization of epidemic models with differential susceptibility and differential infectivity under a general setup. Specifically, we investigate the global asymptotic behavior of equilibria of these systems when the network configuration of the Susceptible-Infectious interactions is strongly connected. These results prove two conjectures by Bonzi et al. (J Math Biol 62:39–64, 2011) and Hyman and Li (Math Biosci Eng 3:89–100, 2006). Moreover, we consider the scenario in which the strong connectivity hypothesis is dropped. In this case, the model exhibits a wider range of dynamical behavior, including the rise of boundary and interior equilibria, all based on the topology of network connectivity. Finally, a model with multidirectional transitions between infectious classes is presented and completely analyzed.

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Acknowledgements

I would like to thank Fred Brauer and Carlos Castillo-Chavez for inspiring me to analyze models involving multiple susceptible classes. Their suggestions brought this project to life and the idea became endemic in my thoughts. I am grateful for Fred’s availability during his visits to Arizona State University and the many meaningful conversations we had. I want to thank one reviewer for valuable comments and suggestions that led to an improvement of the original manuscript.

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  1. Department of Mathematics, California State University, Fullerton, CA, 92831, USA

    Derdei M. Bichara

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Correspondence to Derdei M. Bichara.

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In memory of Fred Brauer.

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Bichara, D.M. Characterization of differential susceptibility and differential infectivity epidemic models. J. Math. Biol. 88, 3 (2024). https://doi.org/10.1007/s00285-023-02023-2

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  • DOI: https://doi.org/10.1007/s00285-023-02023-2

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