Global Stability and Sensitivity Analysis of a Conjunctivitis Epidemic Model in Two Populations with Patient Isolation, Treatment and Insecticide Control

Abstract

Conjunctivitis (pink eye) is a conjunctive infection. It is caused by viruses, bacteria, or allergies. In this study, we present and analyze a conjunctivitis model that includes the consequences of patient isolation, treatment control, and insecticide control. This SIR-SI (susceptible, infected, recovery - susceptible, infected) model describes disease transmission between humans and fly populations. The proposed model is examined using the standard method. The next generation matrix approach is used to calculate the basic reproductive number. The Lyapunov function is applied to determine the model’s stability. The disease-free equilibrium point (DFE) is global asymptotically stable if , whereas the endemic equilibrium point (EE) is global asymptotically stable if  In addition, a sensitivity analysis of the model is performed to determine the significance of model parameters on disease transmission. According to DFE's sensitivity analysis, the effectiveness of patient isolation or human-fly contact prevention is the most sensitive parameter. The numerical results are used to support the theoretical findings. It has been determined that when the effectiveness of patient isolation and recovery of infected humans who visit the doctor increases, the number of infected humans decreases. Furthermore, when the effectiveness of insecticides to protect flies increases, the number of infected flies also decreases.