Subthreshold coexistence of strains: the impact of vaccination and mutation

Maia Martcheva; Mimmo Iannelli; Xue-Zhi Li; Maia Martcheva; Mimmo Iannelli; Xue-Zhi Li

doi:10.3934/mbe.2007.4.287

Mathematical Biosciences and Engineering

2007, Volume 4, Issue 2: 287-317. doi: 10.3934/mbe.2007.4.287

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Subthreshold coexistence of strains: the impact of vaccination and mutation

1.
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105
2.
Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento)
3.
Department of Mathematics, Xinyang Normal University, Henan 464000, P.R.

Received: 01 January 2006 Accepted: 29 June 2018 Published: 01 February 2007
MSC : 92D30.

We consider a model for a disease with two competing strains and vaccination. The vaccine provides complete protection against one of the strains (strain 2) but only partial protection against the other (strain 1). The partial protection leads to existence of subthreshold equilibria of strain 1. If the first strain mutates into the second, there are subthreshold coexistence equilibria when both vaccine-dependent reproduction numbers are below one. Thus, a vaccine that is specific toward the second strain and that, in absence of other strains, should be able to eliminate the second strain by reducing its reproduction number below one, cannot do so because it provides only partial protection to another strain that mutates into the second strain.
Citation: Maia Martcheva, Mimmo Iannelli, Xue-Zhi Li. Subthreshold coexistence of strains: the impact of vaccination and mutation[J]. Mathematical Biosciences and Engineering, 2007, 4(2): 287-317. doi: 10.3934/mbe.2007.4.287

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Abstract

We consider a model for a disease with two competing strains and vaccination. The vaccine provides complete protection against one of the strains (strain 2) but only partial protection against the other (strain 1). The partial protection leads to existence of subthreshold equilibria of strain 1. If the first strain mutates into the second, there are subthreshold coexistence equilibria when both vaccine-dependent reproduction numbers are below one. Thus, a vaccine that is specific toward the second strain and that, in absence of other strains, should be able to eliminate the second strain by reducing its reproduction number below one, cannot do so because it provides only partial protection to another strain that mutates into the second strain.
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