Study of dynamic behaviour of psychological stress during COVID-19 in India: A mathematical approach

In this study, a new attempt has been made using mathematical modelling to study dynamic behaviour and estimate the final size of spread of the psychological stress arising due to sudden outbreak of COVID-19 in India. The proposed mathematical model examines and includes different behaviours of transition from one process to another in current situation and study their propagation mode. We propose a mathematical model, where two different type of psychological stresses occur due to COVID-19 situation and its impact on people's life such as their mental well being and happiness. We present some sufficient conditions for the vanishing or spreading of the psychological stress through qualitative and quantitative analysis. The basic reproduction number ( $$ ) of the model is computed and the local and the global stabilities of different equilibria are studied. Moreover, to better understand the level of psychological stress and decreasing mental well-being during the COVID-19 outbreak in India, we also conducted an online survey. Our findings establish several factors associated with level of psychological impact and mental health status. Based on the empirical analysis, we found that psychological stress has a significant negative influence on mental well being. Further, this study confirms that coping strategies with stress have significantly contributed towards the betterment in the mental well-being of the people. Numerical simulations are also given to illustrate the theoretical results. The results of the present study can be generalized to the society, Government, and others that they can adopt different strategies to avoid stressful situations during COVID-19 outbreak. The findings suggest that policy-makers, Government officials should focus on coping strategies to combat with pandemic disease.