A singularly perturbed vector‐bias malaria model incorporating bed net control.

A malaria transmission disease model with host selectivity and insecticide‐treated bed nets (ITNs), as an intervention for controlling the disease, is formulated. Since the vector is an insect, the vector time scale is faster than the host time scale. This leads to a singularly perturbed model with two distinctive intrinsic time scales, two‐slow for the host and one‐fast for the vector. The basic reproduction number ℜo$$ {\mathfrak{\Re}}_{\mathfrak{o}} $$ is calculated, and the local stability analysis is performed at equilibria of the model when the perturbation parameter ϵ>0$$ \epsilon >0 $$. The model is analyzed when ϵ→0$$ \epsilon \to 0 $$ using asymptotic expansions technique. The results show that if over 30% of humans use ITNs, then ℜo$$ {\mathfrak{\Re}}_{\mathfrak{o}} $$ can be reduced below 1, and hence, malaria disease can be eliminated. In addition, the dynamics on the slow surface indicate that the infected vectors decay fast when ϵ=0.001$$ \epsilon =0.001 $$ according to the numerical simulations. [ABSTRACT FROM AUTHOR]