IJPAM: Volume 88, No. 1 (2013)

MATHEMATICAL MODEL FOR MALARIA TRANSMISSION
DYNAMICS IN HUMAN AND MOSQUITO POPULATIONS
WITH NONLINEAR FORCES OF INFECTION

S. Olaniyi$^1$, O.S. Obabiyi$^2$
$^1$Department of Pure and Applied mathematics
Ladoke Akintola University of Technology
PMB 4000, Ogbomoso, NIGERIA
$^2$Department of Mathematics
University of Ibadan, NIGERIA


Abstract. This paper presents a seven-dimensional ordinary differential equation modelling the transmission of Plasmodium falciparum malaria between humans and mosquitoes with non-linear forces of infection in form of saturated incidence rates. These incidence rates produce antibodies in response to the presence of parasite-causing malaria in both human and mosquito populations.The existence of region where the model is epidemiologically feasible is established. Stability analysis of the disease-free equilibrium is investigated via the threshold parameter (reproduction number $R_{0}$) obtained using the next generation matrix technique. The model results show that the disease-free equilibrium is asymptotically stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. The existence of the unique endemic equilibrium is also determined under certain conditions. Numerical simulations are carried out to confirm the analytic results and explore the possible behavior of the formulated model.

Received: August 15, 2013

AMS Subject Classification: 92B05, 93A30

Key Words and Phrases: mathematical model, malaria, force of infection, reproduction number, antibody, stability

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DOI: 10.12732/ijpam.v88i1.10 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 1