Malaria is a disease caused by the parasite Plasmodium transmitted by the bite of an infected female Anopheles. In general, there are five species of Plasmodium that can cause malaria. Of the five species, Plasmodium falciparum and Plasmodium vivax are two species of Plasmodium that can allow malaria superinfection in the human body. In Indonesia, around 80% of the district/city is still categorized as malaria-endemic, and around 45% population lives in an area at risk of contracting malaria. Various attempts were made by the government to control malaria. One of the strategies carried out is by means of treatment for humans infected with the drug Artemisinin-based Combination Therapies (ACT). In addition, controlling malaria is not only done through treatment for infected humans, but also control of mosquitoes by fumigation.

 

Here in this talk, a malaria superinfection transmission model was constructed considering medical treatment and fumigation interventions. The model constructed as a non-linear ordinary differential equation, which following the transmission diagram given below.

 

Positiveness and boundedness of the system have been proven. Simplification of the model using a Quasi Steady-State Approximation (QSSA) has been used to reduce the dimension of the model into only a 3-dimensional system. The model that has been simplified then were analyzed. The existence of the disease-free equilibrium, endemic of a single strain, and the coexistence equilibrium have been analyzed rigorously. Mathematical analysis of the local stability has been conducted using the linearization approach. Basic reproduction numbers of single strain and invasion reproduction numbers have been shown play an important role in determining the existence and local stability of all equilibrium points.

Numerical analysis regarding the sensitivity and elasticity analysis of all basic reproduction numbers conducted to determine the most influential parameter in the model. Finally, some numerical simulations conducted to show the effect of medical treatment and fumigation on the malaria superinfection elimination program.