Asian Research Journal of Mathematics

In spite of the control measures, malaria remains one of most health challenges of our time and will remain a problem until the transmission agent seize to exist which is impossible. This paper presents a five-dimensional ordinary differential equation modelling the transmission of Plasmodium between Swiss male albino mice that were induced with Plasmodium berghei berghei NK65 and did not recover from the infection, but was suppressed with time to a reasonable level. The study consists of five groups of five Swiss mice each. Group A, B, C and D were healthy mice, infected mice without treatment, infected mice that received chloroquine (5 mg/kg) and infected mice that rwith Plasmodium berghei berghei NK65.eceived mixture of chloroquine (5 mg/kg) and folic acid (5 mg/mL) respectively. Group E mice were infected and administered with 400 mg/kg body weight of Azadirachta indica A. Juss stem extract. The prophylactic activities of the study were performed by administring Swiss mice with chloroquine, folic acid and A. indicastem extract for 3 days. On the 4th day, the mice were inoculated with Plasmodium berghei berghei NK65. The parasite density was estimated for each mouse 72 hours post-parasite inoculation. The standard drug and the extract significantly reduced the parasite. The standard drug and the extract of A. indica ameliorate the effect of the parasite on the liver architecture. In the mathematical model, we perform the analysis of the basic reproductive number R₀ using the next generation matrix, determine the endemic state equilibrium of the model as well the determination of the local and global stability of the model using comparison theorem. Our 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. Numerical simulations were carried out to confirm the analytic results and explore the possible behavior of the formulated model which was in agreement with the experimental analysis of this work.