Modeling and mathematical analysis of fractional order Eye infection (conjunctivitis) virus model with treatment impact: Prelicence and dynamical transmission

In order to comprehend the dynamics of disease propagation within a society, mathematical formulations are essential. Examining how hand contamination might induce pink eye infection (conjunctivitis virus) and treating it early with immunizations is the goal of this research. An immune system-boosting mathematical model is established, and it is converted to a fractional order model by using the Caputo fractional operator. To find the steady position of a recently constructed system SEVIR, a qualitative and quantitative analysis is conducted. Reliable bounded findings are ensured by assessing the generated system's boundedness, positivity, and uniqueness all crucial characteristics of epidemic models. The proposed non-linear system is verified to be present, and a unique solution is shown using fixed-point theorems to validate reliable solutions. Reproductive number with sensitivity analysis of parameters are also determined to verify the rate of spread and see how rate of change of each parameter is most sensitive. Using Lyapunov first derivative functions, the system is examined for local and global stability in order to evaluate the overall effect of early detection strategies and vaccination programs for people with weakened immune systems. Caputo operator is utilized for reliable solution using power law kernel with different fractional values for continuous monitoring of spread of pink eyes infection. Simulations have been made to see the real behavior and effects of pink eyes (conjunctivitis virus) infection to verify that the low immune individuals become strengthen due to early detection and vaccination combine measures. Also identify the true behavior for the control of pink eyes (conjunctivitis virus) infection after early detection and treatment as well as vaccination due to strong immune system of the patients. Investigating the transmission and management of diseases, as well as creating novel control techniques based on our validated findings to stop the conjunctivitis virus from spreading, would be aided by this kind of research.