Mathematical Biosciences and Engineering (MBE)

Epidemic models with nonlinear infection forces

Pages: 267 - 279, Volume 3, Issue 1, January 2006      doi:10.3934/mbe.2006.3.267

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Wendi Wang - Department of Mathematics, Southwest Normal University, Chongqing, 400715, PR, China (email)

Abstract: Epidemic models with behavior changes are studied to consider effects of protection measures and intervention policies. It is found that intervention strategies decrease endemic levels and tend to make the dynamical behavior of a disease evolution simpler. For a saturated infection force, the model may admit a stable disease-free equilibrium and a stable endemic equilibrium at the same time. If we vary a recovery rate, numerical simulations show that the boundaries of the region for the persistence of the disease undergo the changes from the separatrix of a saddle to an unstable limit cycle. If the inhibition effect from behavior changes is weak, we find two limit cycles and obtain bifurcations of the model as the population size changes. We also find that the disease may die out although there are two endemic equilibria.

Keywords:  epidemic, nonlinear incidence, basic reproduction number, stability, cycles.
Mathematics Subject Classification:  92D30.

Received: January 2005;      Accepted: May 2005;      Available Online: November 2005.