On the correlation between variance in individual susceptibilities and infection prevalence in populations

Journal of Mathematical Biology
Alessandro MargheriM Gabriela M Gomes

Abstract

The hypothesis that infection prevalence in a population correlates negatively with variance in the susceptibility of its individuals has support from experimental, field, and theoretical studies. However, its generality has never been formally demonstrated. Here we formulate an endemic SIS model with individual susceptibility distributed according to a discrete or continuous probability function to assess the generality of such hypothesis. We introduce an ordering among susceptibility distributions with the same mean, analogous to that considered in Katriel (J Math Biol 65:237-262, 2012) to order the attack rates in an epidemic SIR model with heterogeneity. It turns out that if one distribution dominates another in this order then it has greater variance and corresponds to a lower infection prevalence for R0 varying in a suitable maximal interval of the form ]1, R0*]. We show that in both the discrete and continuous frameworks R0* can be finite, so that the expected correlation among variance and prevalence does not always hold. For discrete distributions this fact is demonstrated analytically, and the proof introduces a constructive procedure to find ordered pairs for which R0* is arbitrarily close to 1. For continuous distri...Continue Reading

References

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Mar 25, 2009·Journal of Theoretical Biology·Paula RodriguesM Gabriela M Gomes
Aug 11, 2011·Journal of Mathematical Biology·Guy Katriel
Feb 24, 2012·Proceedings. Biological Sciences·M Gabriela M GomesClaudio J Struchiner
Jan 22, 2014·Journal of Theoretical Biology·R I Hickson, M G Roberts
Mar 8, 2014·PLoS Pathogens·M Gabriela M GomesAntonio Coutinho
Aug 15, 2014·PLoS Computational Biology·Delphine PessoaM Gabriela M Gomes

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Citations

Sep 9, 2016·Journal of Mathematical Biology·Tsvetomir TsachevAndreas Widder

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