Bulletin of Mathematical Biology

, Volume 72, Issue 5, pp 1294–1314

Modeling the Dynamics of Viral Evolution Considering Competition Within Individual Hosts and at Population Level: The Effects of Treatment

  • Marcos Amaku
  • Marcelo Nascimento Burattini
  • Francisco Antonio Bezerra Coutinho
  • Eduardo Massad
Original Article

DOI: 10.1007/s11538-009-9495-6

Cite this article as:
Amaku, M., Burattini, M.N., Coutinho, F.A.B. et al. Bull. Math. Biol. (2010) 72: 1294. doi:10.1007/s11538-009-9495-6
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Abstract

We consider two viral strains competing against each other within individual hosts (at cellular level) and at population level (for infecting hosts) by studying two cases. In the first case, the strains do not mutate into each other. In this case, we found that each individual in the population can be infected by only one strain and that co-existence in the population is possible only when the strain that has the greater basic intracellular reproduction number, R0c, has the smaller population number R0p. Treatment against the one strain shifts the population equilibrium toward the other strain in a complicated way (see Appendix B). In the second case, we assume that the strain that has the greater intracellular number R0c can mutate into the other strain. In this case, individual hosts can be simultaneously infected by both strains (co-existence within the host). Treatment shifts the prevalence of the two strains within the hosts, depending on the mortality induced by the treatment, which is, in turn, dependent upon the doses given to each individual. The relative proportions of the strains at the population level, under treatment, depend both on the relative proportions within the hosts (which is determined by the dosage of treatment) and on the number of individuals treated per unit time, that is, the rate of treatment. Implications for cases of real diseases are briefly discussed.

Viral competition Evolution Anti-viral treatment Mutation 

Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  • Marcos Amaku
    • 1
  • Marcelo Nascimento Burattini
    • 2
  • Francisco Antonio Bezerra Coutinho
    • 2
  • Eduardo Massad
    • 2
    • 3
  1. 1.School of Veterinary MedicineUniversity of São PauloSão PauloBrazil
  2. 2.School of MedicineUniversity of São Paulo and LIM01-HCFMUSPSão PauloBrazil
  3. 3.London School of Hygiene and Tropical MedicineLondonUK

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