Control of conjunctivitis virus with and without treatment measures: A bifurcation analysis

Abstract

This study aims to examine the early detection and treatment of conjunctivitis (eye infection) through vaccination and recovery measures, both with and without medication. We develop an immune system-boosting mathematical model and convert it to a fractionally ordered model using the ABC operator. Key properties, such as the uniqueness and boundedness of the model, are investigated using Banach space. To assess the stability of the newly developed SEVIRuRi system and confirm the occurrence of flip bifurcation, we conduct both qualitative and quantitative analyses. We calculate the basic reproductive number, R0, using an advanced approach and analyze its impact across different sub-compartments. Sensitivity analysis is performed on each parameter to understand the rate of change sensitivity. The Atangana–Toufik method is employed to solve the system for various fractional values, providing a reliable bounded solution. Simulations are conducted to observe the real behavior and effects of the conjunctivitis virus, showing that individuals with a strong immune system can recover with or without medication. Finally, we determine the actual state of virus control post-early detection, accounting for treated and untreated individuals due to the robust immune system and precautionary measures.

Keywords

• Mathematical modeling
• Boundedness
• Uniqueness
• Reproductive number “R0”
• Flip bifurcation
• Atangana–Toufik