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2018 A Stochastic Model for Malaria Transmission Dynamics
Rachel Waema Mbogo, Livingstone S. Luboobi, John W. Odhiambo
J. Appl. Math. 2018: 1-13 (2018). DOI: 10.1155/2018/2439520


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.


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Rachel Waema Mbogo. Livingstone S. Luboobi. John W. Odhiambo. "A Stochastic Model for Malaria Transmission Dynamics." J. Appl. Math. 2018 1 - 13, 2018.


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

zbMATH: 07132098
MathSciNet: MR3768208
Digital Object Identifier: 10.1155/2018/2439520

Rights: Copyright © 2018 Hindawi


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