Basic reproduction number for the transmission of Plasmodium vivax malaria

The possibility of relapse is introduced into a mathematical model for the transmission of Plasmodium vivax malaria. In the model, the human population is divided into four classes: susceptible, infected, dormant and recovered. Loss of immunity by individuals in the recovered class moves these individuals back into the susceptible class. Two equilibrium states are found, a disease-free state and an endemic state. A basic reproduction number Ro is found. Depending on whether Ro is less than or greater than one. the disease free state or the endemic state results. The dependence of Ro on the rate of relapse is determined and the implication of this dependence is identified.