When both human and mosquito populations vary, forward bifurcation occurs if
the basic reproduction number R0 is less than one in the absence of disease-induced
death. When the disease-induced death rate is large enough R0 = 1 is a subcritical
backward bifurcation point. The domain for the study of the dynamics is reduced
to a compact and feasible region, where the system admits a speci c algebraic
decomposition into infective and non-infected humans and mosquitoes. Stability
results are extended and the possibility of backward bifurcation is clari ed. A
dynamically consistent nonstandard nite di erence scheme is designed.