Stochastic Optimal Control Model of Haemorrhagic Conjunctivitis Disease
Sacrifice Nana-Kyere *
Department of Mathematics, Valley View University, Kumasi, Ghana.
Desmond Titus Banon
Department of Planning and Budgeting, Dormaa East Assembly, Wamfie, Ghana.
Seth N. Marmah
Department of Mathematics, Methodist Senior/Technical School, Berekum, Ghana.
Daniel Kwarteng
Department of Mathematics, Kibi College of Education, Kibi, Ghana.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Basic reproduction ratio, Pontryagin’s maximum principle, Lagrangian, Hamiltonain, boundary conditions, Stochastic Perturbation, Newton’s method.