A mathematical model of malaria transmission with hospitalized compartment

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Published: Jun 23, 2020
Keywords:
malaria model equilibrium point stability basic reproduction number Hurwitz matrix

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Salinthip Daengkongkho
Faculty of Science and Technology, Pibulsongkram Rajabhat University
Nattakan Maenkrathok
Faculty of Science and Technology, Pibulsongkram Rajabhat University

Abstract

          This study aimed to consider the malaria model of the human and mosquito populations and investigate the equilibrium points of the model at disease free equilibrium point and endemic equilibrium point. Moreover, the stability of the equilibrium points was considered on the conditions of basic reproduction number gif.latex?R_{0}  by using Routh-Hurwitz stability criterion. The results showed that if  gif.latex?R_{0} <1  then disease free equilibrium point was locally asymptotically stable and if  gif.latex?R_{0} >1,  with a sufficient condition then endemic equilibrium point was locally asymptotically stable. The numerical solutions were studied by defining the parameters from the literature researches of the spread of malaria and our assumptions. The numerical analysis revealed that the basic reproduction number at the stability of disease free equilibrium point was gif.latex?R_{0}= 0.7006 which indicated that there was no outbreak of the disease. Finally, if we assume that the proportion of human population bitten by mosquitoes and infected by the virus increases, the probability of mosquito population infected with the virus increased, the recovery rate of hospitalized humans decreased and the rate of hospitalization decreased. Therefore, the results showed that at stability of endemic equilibrium point, the basic reproduction number was gif.latex?R_{0}= 2.50  and the condition which satisfy the Routh-Hurwitz stability criterion for gif.latex?n=4  implied that there was an outbreak of the disease.

Article Details

How to Cite
Daengkongkho, S., & Maenkrathok, N. (2020). A mathematical model of malaria transmission with hospitalized compartment. RMUTSB ACADEMIC JOURNAL, 8(1), 83–99. Retrieved from https://li01.tci-thaijo.org/index.php/rmutsb-sci/article/view/219889
Issue
Vol. 8 No. 1 (2020): January - June 2020
Section
Research Article

Published manuscript are the rights of their original owners and RMUTSB Academic Journal. The manuscript content belongs to the authors' idea, it is not the opinion of the journal's committee and not the responsibility of Rajamangala University of Technology Suvarnabhumi

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