A Simple Macro-model of Covid-19 with Special Reference to India

Motivated by the prevailing severe situation in India, we extend the SIR(S) model of infectious diseases to incorporate demand dynamics and its interaction with Covid-19 spread. We argue that, on one hand, spread of Covid-19 creates panic among consumers and firms and negatively affects economic activity. On the other hand, economy activity intensifies the spread of the infection. Initially assuming that recovered individuals do not develop antibody and become susceptible again, we capture the interaction between economic activity and spread of the disease in a two-dimensional dynamical system. We show that a large fiscal expansion combined with measures to boost community health as well as improve health sector's capacity to provide critical care can at the same time improve the economy and control the spread of the disease. We also find a slightly counter-intuitive result that a fiscal contraction can, under certain conditions, increase output and reduce number of infected individuals. However, we show that such a policy also increases fragility in the system. Finally assuming that only a fraction of recovered individuals become susceptible to contracting the diseases again, we obtain richer dynamics in a three-dimensional dynamical system. The paper also highlights the important role of speed of adjustment in the goods market in stability properties of steady state including emergence of limit cycles