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[00469] A Mathematical and Exploratory Data Analysis of Malaria Disease Transmission Through Blood Transfusion

  • Session Time & Room : 3E (Aug.23, 17:40-19:20) @A511
  • Type : Contributed Talk
  • Abstract : Malaria is a mosquito-borne disease spread by an infected vector (infected female Anopheles mosquito) or through transfusion of plasmodium-infected blood to susceptible individuals. The disease burden has resulted in high global mortality, particularly among children under the age of five. Many intervention responses have been implemented to control malaria disease transmission, including blood screening, Long-Lasting Insecticide Bed Nets (LLIN), treatment with an anti-malaria drug, spraying chemicals/pesticides on mosquito breeding sites, and indoor residual spray, among others. As a result, a SIR (Susceptible - Infected - Recovered) model is developed to study the impact of various malaria control and mitigation strategies. The associated basic reproduction number and stability theory is used to investigate the stability analysis of the model equilibrium points. The global stability of the malaria-free equilibrium is investigated by constructing an appropriate Lyapunov function. By determining the direction of bifurcation, the implicit function theorem is used to investigate the stability of the model endemic equilibrium. Using R and MATLAB, the model is fitted to malaria data from Benue State, Nigeria. Estimates of parameters were made. An optimal control model is then developed and analyzed using Pontryaging's Maximum Principle. The malaria-free equilibrium point is locally and globally stable if the basic reproduction number $(R_{0})$ and the blood transfusion reproduction number $(R_{\alpha})$ are both less or equal to unity. The study of the sensitive parameters of the model revealed that the transmission rate of malaria from mosquito-to-human $(\beta_{mh})$, transmission rate from humans-to-mosquito $(\beta_{hm})$, blood transfusion reproduction number $(R_{\alpha})$ and recruitment rate of mosquitoes $(b_{m})$ are all sensitive parameters capable of increasing the basic reproduction number $(R_{0})$ thereby increasing the risk in spreading malaria disease. The result of the optimal control shows that five possible controls are effective in reducing the transmission of malaria. The study recommended the combination of five controls, followed by the combination of four and three controls is effective in mitigating malaria transmission. The result of the optimal simulation also revealed that for communities or areas where resources are scarce, the combination of Long Lasting Insecticide Treated Bednets $(u_{2})$, Treatment $(u_{3})$, and Indoor insecticide spray $(u_{5})$ is recommended. Numerical simulations are performed to validate the model's analytical results.
  • Classification : 93-xx, 93-10, Mathematical modeling or simulation for problems pertaining to systems and control theory
  • Author(s) :
    • Michael Olaniyi Adeniyi (Lagos State University of Science and Technology)
    • Raphael Oluwaseun Aderele (Lagos State University of Science and Technology )
    • Olajumoke Y Oludoun (Department of Mathematics, Bowen University, Iwo, Nigeria)
    • Matthew Iwada Ekum (Lagos State University of Science and Technology)
    • Segun Isaac Oke (Department of Mathematics, Ohio University, Athens, OH 45701-2979, USA)