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Modelling Infectiology of Dengue Epidemic
Applied and Computational Mathematics
Volume 4, Issue 3, June 2015, Pages: 192-206
Received: May 13, 2015; Accepted: May 26, 2015; Published: Jun. 8, 2015
Authors
Laurencia Ndelamo Massawe, Faculty of Science, Technology and Environmental Studies, the Open University of Tanzania, Dar es Salaam, Tanzania
Estomih S. Massawe, Mathematics Department, University of Dar es salaam, Dar es Salaam, Tanzania
Oluwole Daniel Makinde, Faculty of Military Science, Stellenbosch University, Saldanha, South Africa
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Abstract
In this paper a mathematical model for the transmission dynamics of dengue fever disease is presented. We present a SITR (susceptible, infected, treated, recovery) and ASI (aquatic, susceptible, infected) epidemic model to describe the interaction between human and dengue fever mosquito populations. In order to assess the transmission of Dengue fever disease, the susceptible population is divided into two, namely, careful and careless human susceptible population. The model presents four possible equilibria: two disease-free and two endemic equilibrium.The results show that the disease-free equilibrium point is locally and globally asymptotically stable if the reproduction number is less than unity. Endemic equilibrium point is locally and globally asymptotically stable under certain conditions using additive compound matrix and Lyapunov method respectively. Sensitivity analysis of the model is implemented in order to investigate the sensitivity of certain key parameters of dengue fever disease with treatment, Careful and Careless Susceptibles on the transmission of Dengue fever Disease.
Keywords
Dengue Fever Disease, Careful, Careless, Susceptibles, Equilibrium, Stability, Reproduction Number
Laurencia Ndelamo Massawe, Estomih S. Massawe, Oluwole Daniel Makinde, Modelling Infectiology of Dengue Epidemic, Applied and Computational Mathematics. Vol. 4, No. 3, 2015, pp. 192-206. doi: 10.11648/j.acm.20150403.22
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