Abstract
Dengue disease is caused by four serotypes of the dengue virus: DEN-1, DEN-2, DEN-3, and DEN-4. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV) is a vaccine currently used in Thailand. This research investigates what the optimal control is when only individuals having documented past dengue infection history are vaccinated. This is the present practice in Thailand and is the latest recommendation of the WHO. The model used is the Susceptible-Infected-Recovered (SIR) model in series configuration for the human population and the Susceptible-Infected (SI) model for the vector population. Both dynamical models for the two populations were recast as optimal control problems with two optimal control parameters. The analysis showed that the equilibrium states were locally asymptotically stable. The numerical solution of the control systems and conclusions are presented.
Highlights
The dengue epidemic first occurred in the Philippines in 1954
The disease is caused by an infection by any one of the four serotypes of dengue virus, which are labeled as DEN-1, DEN-2, DEN-3, and DEN-4
We analyzed the effects of different vaccination strategies to prevent secondary dengue infection in order to reduce the severity of the disease
Summary
The dengue epidemic first occurred in the Philippines in 1954. It reached Thailand in 1958. Most of Pongsumpun’s work has been centered on the situation in Thailand since the dengue fever is of major concern to Thailand She has included an exposed class (E) to the model, making the Susceptible-Infected-ExposedRecovered (SEIR) model, to describe the dynamics of the human population. Singh et al [20] and Tasman et al [21] considered the effects of vaccination on a model in which the human population is divided into children and adults They considered that there were two types of infections, primary and secondary dengue infection. The optimal control theory was applied in the transmission model in order to minimize the number of infected humans with primary and secondary infections.
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