Journal of Mathematical Biology

, Volume 51, Issue 6, pp 629-660

First online:

Species Coexistence and Periodicity in Host-Host-Pathogen Models

  • Herbert W. HethcoteAffiliated withDepartment of Mathematics, University of Iowa Email author 
  • , Wendi WangAffiliated withDepartment of Mathematics, Southwest Normal University
  • , Yi LiAffiliated withDepartment of Mathematics, Hunan Normal UniversityUniversity of Iowa

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Models for the transmission of an infectious disease in one and two host populations with and without self-regulation are analyzed. Many unusual behaviors such as multiple positive equilibria and periodic solutions occur in previous models that use the mass-action (density-dependent) incidence. In contrast, the models formulated using the frequency-dependent (standard) incidence have the behavior of a classic endemic model, since below the threshold, the disease dies out, and above the threshold, the disease persists and the infectious fractions approach an endemic equilibrium. The results given here reinforce previous examples in which there are major differences in behavior between models using mass-action and frequency-dependent incidences.

Keywords or Pharses

Coexistence Regulation Host-pathogen Infectious disease Dynamics