ISSN 1119-4618
 

Original Research 


Mathematical Model for the Dynamics of Malaria Transmission Incorporating Vaccine, Protection and Treatment

Samuel Zira John, Hanifa Umar Yusuf, Solomon Alani Usman, Safiyanu Adamu.

Abstract
Malaria is a life threatening disease that is caused by the Plasmodium parasite and transmitted between humans through bites of infected females Anopheles mosquitoes. The aim of this study is to develop a model for the dynamics of malaria under the influence of vaccine, protection and treatment as control strategies with a view to study the effects of these control strategies on the spread of malaria. In developing the model we adopted a vector borne disease transmission interaction, and partitioned the vector-host population into ten compartments, and modelled the interaction dynamics. We finally analyzed the model where the validity of the modified model was proven by establishing a region of invariance and the positivity of solutions. We also established the disease free equilibrium and computed the local stability of the disease free equilibrium point. The reproduction number (a threshold value), R_0 was obtained using next generation matrix. The result of the study ushered in an expression for R_0; where if the reproduction number R_0, is less than 1, then the disease free equilibrium point is stable, so the malaria disease dies out. If the reproduction number R_0 is greater than 1, then the disease free equilibrium point of the model is unstable, so the malaria disease persist in the populations.

Key words: Malaria, Reproduction number, Equilibrium points


 
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How to Cite this Article
Pubmed Style

John SZ, Yusuf HU, Usman SA, Adamu S, . Mathematical Model for the Dynamics of Malaria Transmission Incorporating Vaccine, Protection and Treatment. JPAS. 2020; 20(1): 124-130. doi:10.5455/sf.81437


Web Style

John SZ, Yusuf HU, Usman SA, Adamu S, . Mathematical Model for the Dynamics of Malaria Transmission Incorporating Vaccine, Protection and Treatment. http://www.atbuscienceforum.com/?mno=81437 [Access: March 31, 2020]. doi:10.5455/sf.81437


AMA (American Medical Association) Style

John SZ, Yusuf HU, Usman SA, Adamu S, . Mathematical Model for the Dynamics of Malaria Transmission Incorporating Vaccine, Protection and Treatment. JPAS. 2020; 20(1): 124-130. doi:10.5455/sf.81437



Vancouver/ICMJE Style

John SZ, Yusuf HU, Usman SA, Adamu S, . Mathematical Model for the Dynamics of Malaria Transmission Incorporating Vaccine, Protection and Treatment. JPAS. (2020), [cited March 31, 2020]; 20(1): 124-130. doi:10.5455/sf.81437



Harvard Style

John, S. Z., Yusuf, H. U., Usman, S. A., Adamu, S. & (2020) Mathematical Model for the Dynamics of Malaria Transmission Incorporating Vaccine, Protection and Treatment. JPAS, 20 (1), 124-130. doi:10.5455/sf.81437



Turabian Style

John, Samuel Zira, Hanifa Umar Yusuf, Solomon Alani Usman, Safiyanu Adamu, and . 2020. Mathematical Model for the Dynamics of Malaria Transmission Incorporating Vaccine, Protection and Treatment. Science Forum (Journal of Pure and Applied Sciences), 20 (1), 124-130. doi:10.5455/sf.81437



Chicago Style

John, Samuel Zira, Hanifa Umar Yusuf, Solomon Alani Usman, Safiyanu Adamu, and . "Mathematical Model for the Dynamics of Malaria Transmission Incorporating Vaccine, Protection and Treatment." Science Forum (Journal of Pure and Applied Sciences) 20 (2020), 124-130. doi:10.5455/sf.81437



MLA (The Modern Language Association) Style

John, Samuel Zira, Hanifa Umar Yusuf, Solomon Alani Usman, Safiyanu Adamu, and . "Mathematical Model for the Dynamics of Malaria Transmission Incorporating Vaccine, Protection and Treatment." Science Forum (Journal of Pure and Applied Sciences) 20.1 (2020), 124-130. Print. doi:10.5455/sf.81437



APA (American Psychological Association) Style

John, S. Z., Yusuf, H. U., Usman, S. A., Adamu, S. & (2020) Mathematical Model for the Dynamics of Malaria Transmission Incorporating Vaccine, Protection and Treatment. Science Forum (Journal of Pure and Applied Sciences), 20 (1), 124-130. doi:10.5455/sf.81437