Simulation of a Deterministic Model of HIV Transmission between Two Closed Patches

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James Khobocha Mirgichan
Cyrus Gitonga Ngari
Stephen Karanja


Numerical simulation of a deterministic model of HIV transmission between major cities in Kenya is carried out. The model considered two closed patches connected by the commuter movements of truck drivers being the agents of HIV transmission. The transmission kernel being the function of distance between the patches is ignored. The numerical algorithms are applied in the solution of a nonlinear first-order differential equations. The algorithms are implemented with the aid of MATLAB solver which has an in- built mechanism of Runge Kutta method of fourth order. Numerical simulation indicated the population dynamics of the patches, effect of migration on female sex workers and model reproduction number. The findings of the study were that the migration of the truck drivers between two closed patches contributed significantly to the spread of HIV. In this regard, it was recommended that, stakeholders should target the truck driving population and towns along the transport corridors to mitigate the growing HIV infections and integrate the truck drivers in the national health strategy

Basic reproduction number, HIV/AIDS, MATLAB, migration, Monod function, Runge Kutta

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How to Cite
Mirgichan, J. K., Ngari, C. G., & Karanja, S. (2020). Simulation of a Deterministic Model of HIV Transmission between Two Closed Patches. Journal of Advances in Mathematics and Computer Science, 35(7), 1-11.
Short Research Article


Velten K. Mathematical modeling and Simulation. In introduction for scientists and Engineers (p. 5). Weinheim: John Wiley & sons-VCH verlag GmbH & Co.KGaA; 2009.

Mirgichan James, Cyrus Gitonga, Stephen Karanja. A deterministic model of HIV transmission between two closed patches incorporating the Monod Equation. Mathematical Theory and Modeling. 2019;9(6):1-37. DOI: 10.7176/MTM

Sohaib Attaullah & Muhammad. Mathematical modeling and Numerical simulation of HIV infection model. Results in Applied Mathematics, Open Access. 2020. 7. DOI: 10.1016/j.rinam.2020.100118

Epperson FJ. An Introduction to Numerical methods and Analysis,Second Edition. Hoboken, New Jersey: John Wiley & Sons, Inc; 2013.

Business daily A. Mombasa plans parking yards for trucks to ease; 2019.

KNBS. Population projections. Nairobi-Kenya: KNBS; 2015.

Smith H. (n.d.). In Bacterial growth.