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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
mathematics
A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria
Applied Mathematics and Computation, Volume 195, No. 2, Year 2008
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Description
We formulate a deterministic model with two latent periods in the non-constant host and vector populations, in order to theoretically assess the potential impact of personal protection, treatment and possible vaccination strategies on the transmission dynamics of malaria. The thresholds and equilibria for the model are determined. The model is analysed qualitatively to determine criteria for control of a malaria epidemic and is used to compute the threshold vaccination and treatment rates necessary for community-wide control of malaria. In addition to having a disease-free equilibrium, which is locally asymptotically stable when the basic reproductive number is less than unity, the model exhibits the phenomenon of backward bifurcation where a stable disease-free equilibrium coexists with a stable endemic equilibrium for a certain range of associated reproductive number less than one. From the analysis we deduce that personal protection has a positive impact on disease control but to eradicate the disease in the absence of any other control measures the efficacy and compliance should be very high. Our results show that vaccination and personal protection can suppress the transmission rates of the parasite from human to vector and vice-versa. If the treated populations are infectious then certain conditions should be satisfied for treatment to reduce the spread of malaria in a community. Among the interesting dynamical behaviours of the model, numerical simulations show a backward bifurcation which gives a challenge to the designing of effective control measures. © 2007 Elsevier Inc. All rights reserved.
Authors & Co-Authors
Chiyaka, Christinah
Zimbabwe, Bulawayo
National University of Science and Technology Bulawayo
Tchuenche, J. M.
United States, Arlington
The University of Texas at Arlington
Garira, Winston
Zimbabwe, Bulawayo
National University of Science and Technology Bulawayo
Dube, S.
Zimbabwe, Bulawayo
National University of Science and Technology Bulawayo
Statistics
Citations: 115
Authors: 4
Affiliations: 2
Identifiers
Doi:
10.1016/j.amc.2007.05.016
ISSN:
00963003
Research Areas
Infectious Diseases
Sexual And Reproductive Health