Modelling the impact of plasma therapy and immunotherapy for recovery of COVID-19 infected individuals

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 R_0 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.