An analytical approach to modeling conjunctival viral disease using fuzzy logic and time-delay dynamics

Conjunctivitis, commonly known as pink eye, is the inflammation of the conjunctiva, often accompanied by redness, itchiness, and the discharge of thick white or greyish pus. Highly contagious in settings involving close contact, it poses significant public health and economic concerns. This study proposes a fuzzy mathematical modeling framework to investigate Conjunctival Viral Disease (CVD) transmission dynamics, with particular attention to the roles of asymptomatic carriers and environmental influences. Unlike conventional models that rely solely on deterministic parameters, the incorporation of fuzzy theory allows for representing uncertainties and variabilities inherent in real-world disease transmission. The model further incorporates time-delay terms to account for incubation periods and other latent effects, enhancing the accuracy of system dynamics. This fuzzy framework performs key analyses, including identifying equilibrium points, computation of the basic reproduction number, sensitivity analysis, and assessment of local and global stability. Numerical solutions are obtained using the Forward Euler and Nonstandard Finite Difference (NSFD) methods. The NSFD scheme is rigorously examined for convergence, non-negativity, boundedness, and consistency properties. Simulation results confirm that the NSFD approach maintains the qualitative features of the model even under larger time steps. Overall, the study underscores the importance of integrating fuzzy logic and time delays in epidemic modeling and presents a robust methodological approach for understanding and managing the spread of infectious diseases in uncertain and dynamic environments.