Volume 20, Number 1, Spring 2012
GLOBAL DYNAMICS OF A TWO-STRAIN DISEASE
Dedicated to Herb Freedman on the occasion of his 70th birthday
MODEL WITH LATENCY AND SATURATING
S. M. ASHRAFUR RAHMAN AND XINGFU ZOU
Abstract. This paper deals with a vector-borne disease model containing latency and nonlinear incidence rates. Global dynamics of the model is completely determined by suitable Lyapunov functionals. If the basic reproduction number is less than one, then disease dies out, but if the number is larger than one, we found that one or both of the the strains become endemic. A unique co-endemic equilibrium appears when both the boundary equilibria exist but are unstable, and this in contrast to the situation when mass action incidence is adopted in which co-persistence is impossible and competition exclusion is generic. It is also found that the persistence of a strain not only depends on the respective reproduction number but also depends on the combined parameters and a strain may disappear even though the strain specific reproduction number is larger than one. The higher saturation level of one strain may result in emerge or extinction of the other strain in some situations.