摘要
In this study, we develop an SIS model for two types of mosquitoes, a traditional one and one that is resistant to IRS and ITNs. The resistant mosquito develops behavioral adaptation to control measures put in place to reduce their biting rate. They also bite early before dusk and later after dark when people are outside the houses and nets. We determine the effect of the two types of mosquitoes on malaria transmission in Kenya. The basic reproduction number R <sub>0</sub> is established as a sharp threshold that determines whether the disease dies out or persists in the population. Precisely, if R <sub>0</sub> ≤ 1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out and if R <sub>0</sub> > 1, there exists a unique endemic equilibrium which is globally stable and the disease persists. The contribution of the two types of mosquitoes to the basic reproduction number and to the level of the endemic equilibrium is analyzed.
In this study, we develop an SIS model for two types of mosquitoes, a traditional one and one that is resistant to IRS and ITNs. The resistant mosquito develops behavioral adaptation to control measures put in place to reduce their biting rate. They also bite early before dusk and later after dark when people are outside the houses and nets. We determine the effect of the two types of mosquitoes on malaria transmission in Kenya. The basic reproduction number R <sub>0</sub> is established as a sharp threshold that determines whether the disease dies out or persists in the population. Precisely, if R <sub>0</sub> ≤ 1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out and if R <sub>0</sub> > 1, there exists a unique endemic equilibrium which is globally stable and the disease persists. The contribution of the two types of mosquitoes to the basic reproduction number and to the level of the endemic equilibrium is analyzed.
