Destabilizing effect of the host immune status on the sequential transmission dynamic of the dengue virus infection

A mathematical model describing the sequential transmission dynamics of dengue virus infection in the presence of two serotypes of the virus is developed. Since a dengue infection can lead to an apparent (symptomatic) illness or an in-apparent (asymptomatic) illness, our model allows for a fraction ( p i ) of the population infected by virus ‘ i ’ to exhibit no symptoms of the illness. The model allows for cross-protection of an individual already immune to one virus against a new infection by the other virus. The conditions governing the stabilities of three equilibrium states; a disease free state, a state where only one serotype is present and another state where both serotypes coexist, are obtained. It is found that the conditions depend on the values of the fractions of infected population who exhibit no symptoms. The existence of the last two equilibrium states also depends on degree of cross-protection bestowed by the infection by one serotype against an infection by the other serotype. Our analysis shows that the presence of an in-apparent class of infected individuals or of a degree of cross-protection, can affect the conditions required for the two serotypes to co-exist. It is also found two serotype equilibrium state can be destabilized by increasing the number of asymptomatic ill individuals in the infected population.