Modeling the effectiveness of isolation strategies in preventing STD epidemics
SIAM Journal on Applied Mathematics
Recent advances on determining the number of real roots of parametric polynomials
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Dynamical behavior for a stage-structured SIR infectious disease model
Nonlinear Analysis: Real World Applications
Dynamics of a model of Toxoplasmosis disease in human and cat populations
Computers & Mathematics with Applications
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In this paper, we give the global dynamical behaviors of a reduced SIRS epidemic model with a nonlinear incidence rate @kI^pS^q. We first discuss the qualitative properties of the equilibria in the interior of the first quadrant, and study the bifurcations including saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. Then we consider equilibria at infinity, determining the number of orbits in exceptional directions for the global tendency. In this discussion, the unspecified degree p,q of polynomials and their high degeneracy prevent us from using the methods of blowing-up or normal sectors in some cases. We lastly discuss the existence and uniqueness of limit cycles.