MODEMAT project, funded by the Escuela Politécnica Nacional de Quito ($10.000). Start: January 2015.

Malaria is caused by a protozoan of the genus Plasmodium and transmitted to humans by Anopheles mosquito. Population at risk of malaria live in tropical vulnerable areas, where they are exposed to the mosquitoes carrying the protozoan. Early symptoms of malaria are similar to those of the common flu: headache and joint pain, fever, etc. When the disease reaches advanced stages, it causes anaemia, liver problems and even death.

At this time, Ecuador is in the pre-elimination of malaria stage, according to the annual report of the World Health Organization [WHO]. Reduce the population of mosquitoes that transmit the disease and the exposure of humans to infected mosquitoes are the main strategies to eliminate malaria.

In this projects, we propose to design and simulate optimal control problems of the SEIR (Susceptible-Exposed-Infected-Removed) equations for the two populations of interest: humans and mosquitoes. The control variables will represent strategies such as fumigation and the use of ITNs (insecticide treated nets). These strategies follow the WHO recommendations.

References

• [NS] G. A. Ngwa and W. S. Shu. A mathematical model for endemic malaria with variable human and mosquito populations. Mathematical and computer modelling, 32(7), 747-763.
• [WHO] WHO. World Malaria Report 2013. WHO Malaria Global Program.
• [ST] C. J. Silva and D. F. Torres. An optimal control approach to malaria prevention via insecticide-treated nets. Conference Papers in Mathematics (Vol. 2013). Hindawi Publishing Corporation, 2013.
• [B] J. C. Butcher. The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods. Wiley-Interscience, 1987.
• [BCK] K. Blayneh, Y. Cao and H. D. Kwon. Optimal control of vector-borne diseases: treatment and prevention. Discrete and Continuous Dynamical Systems B, 11 (2009), 587-611.