American Institute of Mathematical Sciences

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2007, 4(2): 287-317. doi: 10.3934/mbe.2007.4.287

Subthreshold coexistence of strains: the impact of vaccination and mutation

Maia Martcheva 1, , Mimmo Iannelli 2, and  Xue-Zhi Li 3,

1. 

Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, United States
2. 

Dipartimento di Matematica, Università di Trento, 38050 Povo (Trento), Italy
3. 

Department of Mathematics, Xinyang Normal University, Henan 464000, P.R., China

Received  January 2006 Revised  December 2006 Published  February 2007

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.
Keywords: latent stage, coexistence, strongly subthreshold coexistence, vaccine enhanced pathogen polymorphism., multiple coexistence equilibria, multiple endemic equilibria, mutation, backward bifurcation, latent-stage progression age structure, alternating stability, vaccination.
Mathematics Subject Classification: 92D3.
Citation: Maia Martcheva, Mimmo Iannelli, Xue-Zhi Li. Subthreshold coexistence of strains: the impact of vaccination and mutation. Mathematical Biosciences & Engineering, 2007, 4 (2) : 287-317. doi: 10.3934/mbe.2007.4.287
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