Stability Analysis of a two-strained Dengue Infection Dynamic Model Incorporating Vector Controls and Vaccination
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Abstract
A modified mathematical model for the transmission dynamics of a two-strain dengue infection in a population is designed and vividly analysed. The model incorporates vector control measures such as good environmental sanitation and use of mosquito treated nets to reduce mosquito density and bite respectively. Also incorporated in the work is the addition of vaccines to treatment at secondary infection stage to ensure recovery with long term immunity. The reproduction number was computed using the next generation matrix method. Bifurcation analysis reveals a backward bifurcation at , indicating that the disease persistence is possible even when The results of the analysis show that the Disease-Free Equilibrium (DFE) is both locally and globally asymptotically stable via Rout-Hurwitz and Lyapunov criteria. In the absence of the vector control measures and vaccination, the model exhibits a unique endemic equilibrium whenever the reproduction threshold exceeds unity (. while in the presence of the control measures, the reproduction number reduces below unity (
Keywords
- Dengue
- perturbation
- reproduction number
- optimal control
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