The impact of vaccination on COVID-19 an‎d fractional order-based dynamic modeling

1/1/1900 12:00:00 AM

This thesis investigates the effect of vaccination on the transmission dynamics of the COVID-19 disease using a mathematical model based on time-fractional derivatives. A novel fractional-order epidemic model is developed an‎d analyzed by incorporating a compartment for vaccinated individuals (V). Initially, the COVID-19 vaccine model is formulated using integer-order differential equations. Subsequently, the Caputo-type derivative is applied to extend the model to a fractional case, an approach that allows for the inclusion of the memory effect in modeling the spread of infectious diseases. Using the nonlinear least-squares method, the model is fitted to reported real-world data from Pakistan, an‎d several of the modelʹs parameters are estimated from this data. The basic reproduction number (R_0) is calculated using the next-generation matrix method. A detailed mathematical analysis of the fractional model is comprehensively discussed, including the investigation of the invariant region, the positivity of the modelʹs solutions, the eva‎luation of equilibrium points (disease-free an‎d endemic), an‎d the analysis of their local an‎d global stability. An efficient iterative method is used for the numerical solution of the model, which is then simulated to assess the impact of vaccination. The influence of key parameters on the pan‎demicʹs dynamics is illustrated graphically. Furthermore, the effect of various intervention scenarios on disease incidence is demonstrated. It has been found that reducing the effective contact rate (by up to 30%), enhancing the vaccination rate (by up to 50%), an‎d decreasing the rate of immunity loss (by up to 30%) from their current baseline values significantly reduce new cases of the disease. Moreover, a combination of intervention strategies demonstrates higher efficacy in controlling an‎d even eliminating the disease. This thesis has been developed based on the work presented in reference [1].

مدل‌سازي رياضي , COVID-19 , واكسيناسيون , مشتق كسري كاپوتو , تحليل پايداري , شبيه‌سازي عددي

Mathematical Modeling , COVID-19 , Vaccination , Caputo Fractional Derivative , Stability Analysis , Numerical Simulation

Milad Heidari Azar

Jalil Rashidinia