Investigation of SEIR model with vaccinated effects using sustainable fractional approach for low immune individuals

Mathematical formulations are crucial in understanding the dynamics of disease spread within a community. The objective of this research is to investigate the SEIR model of SARS-COVID-19 (C-19) with the inclusion of vaccinated effects for low immune individuals. A mathematical model is developed by incorporating vaccination individuals based on a proposed hypothesis. The fractal-fractional operator (FFO) is then used to convert this model into a fractional order. The newly developed SEVIR system is examined in both a qualitative and quantitative manner to determine its stable state. The boundedness and uniqueness of the model are examined to ensure reliable findings, which are essential properties of epidemic models. The global derivative is demonstrated to verify the positivity with linear growth and Lipschitz conditions for the rate of effects in each sub-compartment. The system is investigated for global stability using Lyapunov first derivative functions to assess the overall impact of vaccination. In fractal-fractional operators, fractal represents the dimensions of the spread of the disease, and fractional represents the fractional ordered derivative operator. We use combine operators to see real behavior of spread as well as control of COVID-19 with different dimensions and continuous monitoring. Simulations are conducted to observe the symptomatic and asymptomatic effects of the corona virus disease with vaccinated measures for low immune individuals, providing insights into the actual behavior of the disease control under vaccination effects. Such investigations are valuable for understanding the spread of the virus and developing effective control strategies based on justified outcomes.