Mathematical modeling of COVID-19 in India and Nepal with optimal control and sensitivity analysis

The pandemic started in the late 2019 and is still waving in claiming millions of lives with virus being mutated to deadlier form. This pandemic has caught attention toward interventions like improved detection of the infected, better quarantine facilities and adequate medical facilities in terms of hospital beds and other medical aid. In this study, we developed a 7-compartment epidemiological model, with inclusion of identified and unidentified infected population along with media factor associated with the aware identified infected population. This is included by using Holling function in the nonlinear incidence, that is responsible for reduction in infection rate via identified infected. The model is fitted to the observed active COVID-19 cases data, collected for a period of 11 months between July 2020 to May 2021 of Nepal and India, and the infection rate as well as the basic reproduction number is obtained for the first wave and second wave of the pandemic in both countries. A comparative analysis on the effect of different parameters on the disease prevalence for both the countries is presented in this work. Sensitivity analysis, time series behavior and optimal control analysis with control parameters equating with reduced infection rate, enhanced detection rate, improved quarantine and hospitalization rate are presented in detail. By means of PRCC, sensitivity analysis is performed and the key parameters influencing the disease prevalence are identified. A detailed study on impact of several parameters in the COVID-19 prevalence, thereby suggesting the interventions to be implemented is discussed in the work. Predictions till June 30, 2021, are obtained using the second wave data for both the countries, and a declining trend is observed for both the countries for the next 30 to 40 days. The estimated values of the infection rates and the hospitalization rates obtained are higher for India compared to Nepal. An optimal control analysis for both the countries is described in detail providing the difference in infectives and recoveries with and without any controls or interventions. The study suggests that improved treatment facilities, testing drives and other non-pharmaceutical interventions would bring down the infected cases to a major extent.