American Institute of Mathematical Sciences

Advanced
2006, 3(1): 267-279. doi: 10.3934/mbe.2006.3.267

Epidemic models with nonlinear infection forces

Wendi Wang 1,

1. 

Department of Mathematics, Southwest Normal University, Chongqing, 400715, PR, China

Received  January 2005 Revised  May 2005 Published  November 2005

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: basic reproduction number, epidemic, cycles., stability, nonlinear incidence.
Mathematics Subject Classification: 92D3.
Citation: Wendi Wang. Epidemic models with nonlinear infection forces. Mathematical Biosciences & Engineering, 2006, 3 (1) : 267-279. doi: 10.3934/mbe.2006.3.267
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