Massawe, Laurencia Ndelamo
(2017)
Modelling Infectiology and Optimal Control of Dengue Fever Disease Epidemics in Tanzania.
["eprint_fieldopt_thesis_type_phd" not defined] thesis, The Open University of Tanzania.
Abstract
A mathematical model for infectiology and optimal control of dengue fever disease epidemics in Tanzania is formulated and analysed. The model describes the interaction between human and dengue fever mosquito populations with treatment. Susceptible human population is divided into two, namely, careful and careless susceptible. The model presents two disease-free and two endemic equilibrium points. 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.
The model is fitted to data on dengue fever disease using maximum likelihood estimator. From the results, it is observed that the forecasted data closely agree to the actual data. Sensitivity analysis of the model is implemented in order to investigate the sensitivity of certain key parameters of dengue fever disease transmission.
Moreover the model consists of five control strategies that is campaign aimed in educating careless individuals, reducing mosquito-human contact, removing vector breeding places, insecticide application and the control effort aimed at reducing the maturation rate from larvae to adult. Optimal Control (OC) approach is used in order to find the best strategy to fight the disease and minimize the cost. From the cost-effectiveness analysis, the results suggest that combination of removing vector breeding places and reducing maturation rate from larvae to adult is the most cost-effective of all the strategies for dengue fever disease control considered.
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