Mathematical modelling of the transom Dynamics of dengue with logs Human population growth

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University of Dar es Salaam
The purpose of this study was to investigate the transmission dynamics of dengue disease with a logistic human population growth. A vector host model of a system of differential equation was formulated. The equilibrium points were determined and it was observed that the disease free equilibrium point is asymptotically stable when a reproduction number is less than unity and unstable when reproductive number is greater than unity. In the analysis of the model, Centre manifold theory was used to analyse the local stability of endemic equilibrium and it was observed that the model undergoes a forward bifurcation at reproduction number equal to unity. For the sensitivity analysis, it was observed that the biting rate is the most sensitive parameter on the reproduction number while the birth rate was observed to be least sensitive parameter. The numerical analysis of the model was carried out and it was observed that susceptible human population decreases with time as many people get infections from infective mosquitoes. The susceptible mosquitoes increase because of climate changes and lack of people awareness and knowledge about how to control the disease. The observation of the biting rate being the most effective parameter for production of secondary infections, has proved in the simulations that there are a great number of infective mosquitoes that reduces human susceptible population and increases the infected ones and so the transmission of dengue fever may become epidemic.
Available in printed form, East Africana Collection, Dr. Wilbert Chagula Library, Class mark (THS EAF RC137.P36)
Dengue, Population, Mathematical models
Pande, J. (2013) Mathematical modelling of the transom Dynamics of dengue with logs Human population growth, Master dissertation, University of Dar es Salaam. Dar es Salaam.