| Abstract: | This paper proposes a Susceptible-Infective-Susceptible (SIS)
model to study the malaria transmission with treatment by considering logistic
growth of mosquito population. In this work, it is assumed that the treatment
rate is proportional to the number of infectives below the capacity and is
constant when the number of infectives is greater than the capacity. We find
that the system exhibits backward bifurcation if the capacity is small and it
gives bi-stable equilibria which makes the system more sensitive to the initial
conditions. The existence and stability of the equilibria of the model are
discussed in detail and numerical simulations are presented to illustrate the numerical results. |
