Vaccination model for visceral leishmaniasis with infective immigrants

In this paper, we present and analyzed a mathematical model that describes the dynamics of visceral leishmaniasis in a population with immigration of infective humans under mass vaccination strategy. Our result shows that in order for the vaccine to play a role on disease control, it must be very effective. Results also show that vaccination coverage does not have any impact on disease control when the immigration rate is small, and it does not affect the long-term behavior when the immigration rate is high. In the case of no immigration of infective, our system has disease-free equilibrium, and it is globally asymptotically stable when R0, the basic reproduction number, is less than unity. Numerical simulation shows that in the case of no immigration of infective, our system undergoes forward bifurcation when R0 passes throw unity.