Analysis of an ODE Model for Conjunctivitis Spread With Risk Assessment

Conjunctivitis is a very infectious ocular disease that is transmitted both directly and indirectly, thus making it necessary to study control strategies for the disease. A deterministic nonlinear model is proposed to describe the process of transmission of conjunctivitis using both primary and secondary infection rates. The models that have been proposed so far can be made more realistic with the help of incorporating a compartment called “risk assessment†where the individuals at risk can take preventive actions like screening and awareness against contracting the disease. These individuals are taken to be those susceptible to infection. The model incorporates the use of saturated incidence rates to represent behavioral and environmental constraints on transmission. First of all, the basic properties of the model are analyzed. It can be seen that the model is well posed, that is, the solution of the model exists, is unique, and bounded for all time. The basic reproduction number for the disease can be found using the next generation matrix. A sensitivity analysis is done to detect the most significant parameters impacting the dynamics of disease transmission. Stability characteristics of equilibria are analyzed using Lyapunov techniques. The stability analysis of a second order is further used to ensure robustness of the global dynamics under disturbances. Finally, numerical simulations are run to verify the analytical results and analyze the effect of risk assessment and compliance with behavior. The findings reveal that the disease-free equilibrium is globally stable if R0 1. It is found that increasing the risk assessment rate and decreasing the number of contacts between individuals reduce considerably the disease prevalence, and hence it highlights the significance of preventive measures in controlling the spread of conjunctivitis. The main contribution of the current study is in combining a risk assessment procedure with thorough analyses and simulations, which offer more realistic modeling of conjunctivitis transmission than other previous studies.