Stochastic Optimal Control Model of Haemorrhagic Conjunctivitis Disease
Sacrifice Nana-Kyere, Desmond Titus Banon, Seth N. Marmah, Daniel Kwarteng
Journal of Advances in Mathematics and Computer Science · pp. 1–19 · Published 27 Mar 2019
10.9734/jamcs/2019/v31i330113Abstract
In this research article, a model for the transmission dynamics of haemorrhagic conjunctivitis disease is presented. The tool of dynamical system is employed in investigating the potency of the spreading of the epidemic. The analysis revealed the likelihood of the epidemic to spread when the basic reproduction number exceeds one. The model is reformulated as optimal control problem to assess the effectiveness of the proposed control strategy. Maximum Principle was employed to derive the necessary conditions for the existence of optimal control. Numerical solution of the optimality was derived and computed to investigate the optimum control strategy that would be efficacious to be implemented in reducing the number of exposed and infected individuals. Stochastic version of the model is deduced by introducing stochastic perturbations in the deterministic one. Numerical simulations are provided to illustrate the differences in the dynamics of the models and to understand the epidemic phenomenon.
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