Dynamical Modelling and Optimal Control of Conjunctivitis Epidemic

In this study, we develop a mathematical model for conjunctivitis transmission dynamics. We fit the model to the incident cases in Singapore. We obtain the positivity and boundedness of the proposed model, the qualitative basic reproduction number, (Formula presented.). We obtained both the local and global stability of the conjunctivitis-free and present equilibrium under various scenarios. Using the Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficient (PRCC), an uncertainty and robustness analysis sensitivity study was performed to determine the model's parameters that affect the (Formula presented.) and cause susceptibility in its estimation and dynamics of peak infection, time to peak infection, final epidemic size, and the (Formula presented.). The outcome of the sensitivity analysis was applied to develop an intervention model. With the approach of the Pontryagin maximum principle, the intervention model was solved for optimality. Numerical simulations with in-depth cost analyses are provided so that the model can complement the analytic analyses. The study showed that Policy D, which constitutes personal protection and disinfection of the environment, has an advantage over the other policies, offering the least investment but a substantial number of infections subdued. This means that the prevalence of the disease in Singapore will be reduced when personal hygiene and environmental disinfection are employed. The results of the study will serve as a contemporary framework for public health in examining mitigation strategies for the disease in high-risk communities.