MODELING DIRECT AND INDIRECT TRANSMISSION OF CONJUNCTIVITIS WITH NON-MONOTONIC AND SATURATED INCIDENCE: STABILITY AND CONTROL ANALYSIS

This paper presents an analysis of control strategies applied to a deterministic compartmental model for conjunctivitis (viral/bacterial eye flu). The proposed model is novel in the way that it takes into account both the direct (human-to-human) and the indirect (environment-to-human) transmission of the disease by incorporating infectious density-induced force of infection and saturated incidence rate function, respectively. Alongside examining essential qualitative characteristics of the model like positivity and boundedness, we also obtain the basic reproductive threshold, [Formula: see text] and analyze the effect of various crucial parameters on [Formula: see text] using normalized sensitivity indices. The existence and stability (local and global) of conjunctivitis-free and endemic equilibrium are also discussed. Further, two time-dependent measures, prevention (to reduce direct transmission) and hygiene compliance (to reduce indirect transmission), are introduced as control within the model to formulate an optimal control problem (OCP). The existence and characterization of optimal controls are proved and the OCP is solved using the fourth-order Runge–Kutta method in forward and backward directions. The comparative study suggests that while the application of individual control measures is effective and complements each other, however, the most cost-efficient approach to rapidly reduce eye flu infection is the simultaneous implementation of both control measures. This paper provides valuable insights that can be useful in crafting precise and impactful synergy for managing conjunctivitis and disseminating awareness accordingly.