Modelling the effect of sterile insect technology for control of anopheles mosquito population in Tanzania

Sterile insect technology (SIT) is a method of biological control that uses sterile male insects to reduce the reproductive rate of a species of target insect. The method relies on the release of sterile or treated males in order to reduce the native population of insects. We discuss the suitability of this release technique when applied to anopheles mosquitoes that transmit malaria disease. Understanding the control measures that should be taken to control the disease is key to prevent its spread. Dorta et al., 1993 showed that the use of chemical strategies in vector control around the world is problematic and largely ineffective because they can induce mosquito resistance and are detrimental to the biodiversity hampering its effectiveness. It is therefore necessary to develop and test new control tools that are more sustainable. A mathematical model for the dynamics of anopheles mosquito population (DAMP) is formulated and analysed. In particular, we propose and analyse a new model (SIT Model) that considers the release of treated male mosquitoes to assess its effectiveness in control of wild mosquito population. We establish the basic offspring number (R) that will be used together with the concepts of Jacobian matrices, Routh-Hurwitz criterion, cooperative systems and additive compound matrices to conclude on the stability of equilibrium points. Numerical simulations for the DAMP and SIT models, using Nonstandard Finite Difference (NSFD) numerical schemes are provided. The results indicate that SIT with frequent and high rate of release can be an alternative to chemical control tools.