Analysis of a Dengue Disease Transmission Model without Immunity

Abstract

A dengue disease transmission model by Esteva and Vargas assumes that once a person recovers from the disease he or she will not be reinfected by the disease. However recovering from one of the four types of virus will not guarantee that a person is immuned to the other types. Hence it is reasonable to assume that the immune subpopulation is negligible. Consequently the model is reduced to a two-dimensional planar system. In this model, the endemic state is stable if the basic reproductive number of the disease is greater than one, and this result is similar to the result of the transmission model with immunity. For a relatively small series of outbreaks of the disease in population sufficiently large for the number of susceptible to remain effectively constant, the model is reduced to a population model for the group of infectives. Taking the incubation period into consideration, the model without immunity gives rise to a two-dimensional delay differential equations. The presence of the delay seems to destabilise the dynamics Keywords: Dengue disease; immunity; host-vector model; locally stable; globally stable; thresold parameter; delay.