Journal of Applied Mathematics

A Stochastic Model for Malaria Transmission Dynamics

Rachel Waema Mbogo, Livingstone S. Luboobi, and John W. Odhiambo

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Abstract

Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis). In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp). The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.

Article information

Source
J. Appl. Math., Volume 2018 (2018), Article ID 2439520, 13 pages.

Dates
Received: 14 September 2017
Accepted: 26 December 2017
First available in Project Euclid: 17 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.jam/1521252012

Digital Object Identifier
doi:10.1155/2018/2439520

Mathematical Reviews number (MathSciNet)
MR3768208

Citation

Mbogo, Rachel Waema; Luboobi, Livingstone S.; Odhiambo, John W. A Stochastic Model for Malaria Transmission Dynamics. J. Appl. Math. 2018 (2018), Article ID 2439520, 13 pages. doi:10.1155/2018/2439520. https://projecteuclid.org/euclid.jam/1521252012


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