ABSTRACT
Coronavirus disease 2019 (COVID-19), an infection that is highly contagious. It has a regrettable effect on the world and has resulted in more than 4.6 million deaths to date (July 2021). For this contagious disease, numerous nations implemented control measures. Every country has vaccination programs in place to achieve the best results. This research is done in two stages, including partial and complete vaccination, to enhance the efficiency and effectiveness of the vaccination. Our study found that receiving this vaccination lowers the risk of contracting a disease and its side effects, such as severity, hospitalization, need for oxygen, admission to the intensive care unit, and infection-related death. Taking into account, the system is built using fractional-order Caputo sense nonlinear differential equations. A basic reproduction number is calculated to determine the transmission rate. The bifurcation analysis predicts chaotic behavior of a system for this threshold value. The suggested system's recovery rate is optimized using fractional optimum controls. For the fractional-order differential equation, numerical results are simulated using MATLAB software using real-validated data (July 2021).
ABSTRACT
Since the first case of COVID-19 was detected in Wuhan, China in December 2019, COVID-19 has become a pandemic causing a global economic and public health emergency. There is no known treatment or vaccine available for COVID-19 during the initial period of the outbreak. Immunotherapy and plasma therapy has been used with satisfactory efficacy over the past two decades in many viral infections like SARS (Systemic Acute Respiratory Syndrome), MERS (Middle East Respiratory Syndrome) and H1N1. Limited data from China show clinical benefit, radiological resolution, reduction in viral loads and improved survival. We aim to create a mathematical model for COVID-19 transmission and then apply various control parameters to see their effects on recovery from COVID-19 disease. We have formulated a system of non-linear ordinary differential equations, calculated basic reproduction R0 and applied five different controls (self-isolation, quarantine, herd immunity, immunotherapy, plasma therapy) to test the effectiveness of plasma therapy. Control optimality was checked by Lagrangian functions. Numerical simulations and bifurcation analysis were carried out. The study concludes that the COVID-19 outbreak can be controlled up to a significant level in three weeks after applying all the control strategies together. These strategies lead to reduction in hospitalization and a rise in recovery from infection. Immunotherapy is highly effective initially in hospitalized infected individuals however better results were seen in the long term with plasma therapy.
