MODELING THE EFFECT OF PERIODIC TEMPERATURE ON MALARIA TRANSMISSION DYNAMICS
R. M. NDUNG’U
Department of Mathematics and Physical Sciences, Dedan Kimathi University of Technology, Kenya and School of Mathematics, University of Nairobi, Kenya
G. P. POKHARIYAL *
School of Mathematics, University of Nairobi, Kenya
R. O. SIMWA
School of Mathematics, University of Nairobi, Kenya
*Author to whom correspondence should be addressed.
Abstract
Malaria transmission depends on the survival, life-history parameters and population dynamics of adult Anopheles mosquitoes. These parameters and dynamics are sensitive to a number of factors key among them being the temperature. Temperature variation plays an important role in influencing the dynamics as it causes fluctuation of biting rate, mosquito death rate and the rate of progression from exposed to the infectious class. A model incorporating periodic temperature fluctuations is developed and existence of equilibrium states proved. The mosquito population abundance peaks with increasing temperature and disease endemicity depends on the degree of variation of temperature. Our results points to the importance of implementing intervention strategies, aimed at reducing malaria risk and eventually eliminating the disease, during the low temperature seasons.
Keywords: Endemic malaria, transmission, temperature, basic reproduction number, disease-free equilibria