The pandemic being a health issue at its core is a multifaceted crisis encompassing both economic and epidemic factors in a twisted tale of challenges. In counteraction, we have proposed a combined epidemic-economic model that analyses system dynamics arising in the presence of an infectious disease (SARS-2-COVID-19 in our case). Dynamical analysis of the system has been performed in context to the equilibria along with local and global stability analysis of the system simultaneously visualizing the effect on capital stabilization. The global stability analysis has been performed using graph-theoretic method. Curve-Fit has been performed for the system using optimization algorithm. The relation between all the parameters and variables involved in the model has been explored by calculating sensitivity indices which gives us the proportion that a relative change in a parameter brings to the relative change in a variable. Our findings reveal that (1) Vaccination instigates economic growth (with evidence of data obtained for 24 countries). (2) Complete vaccination leads to a considerable reduction in all infections (reduction up to 90%, as per current CDC study). (3) Excessive exposure to media can facilitate spike in infections. (4) Parameter sensitivity analysis can be of immense help in policy formation. 

/pdf/analysing-an-epidemic-economic-model-in-the-presence-of-18f0ql74.pdf

Analysing an epidemic–economic model in the presence of novel corona virus infection: capital stabilization, media effect, and the role of vaccine

In this paper, we analyze a delayed SIR epidemic model with saturated incidence rate. Our goal in this model is to introduce the incubation period into susceptible and infectious individuals in the incidence rate. The dynamics are studied in terms of local stability and of the description of the Hopf bifurcation, that is proven to exist as the delay (taken as a parameter of bifurcation) cross some critical value. Additionally we conclude with a numerical
illustrations.

Hopf Bifurcation Analysis In a Delayed SIR Model

The described model of economic growth under conditions of an epidemic does not directly refer to the social and economic situation in the years 2020 and 2021, i.e. to the COVID-19 pandemic. It is aimed to identify the consequences of any epidemic leading to severe social losses (high percentages of the infected and dead, limited interpersonal contacts as a result of lockdown, a lowered level of general individual and social well-being) and economic losses (a fall in production as a result of the collapse of aggregate demand and a reduction in the supply capacity of the economy, and consequently a decreased rate of capital accumulation). The described epidemiological-economic model combines the SIR epidemiological model from 1927 (with its modification proposed in 2020 by Bärwolff) and the neoclassical growth model proposed by Solow in 1956. The authors expanded the concept by lockdown restrictions with various levels of their severity, considering specific rules for their implementation, and by guidelines for scenario analyses of changes in the value of social and economic activity index, in the value of aggregate production, in the capital stock accumulated in the economy and in social utility. The effect of an epidemic on medium-term economic growth was also considered, for various levels of economic development (measured by the distance of input capital stock from that formed in a long-term equilibrium in the Solow model). The principal conclusions drawn from the discussion are listed below. First, the introduction of the same restrictions imposed on social and economic activity throughout the territory of a country poses a considerable risk of error in assuming a uniform spread of the epidemic. Second, a rapid introduction of lockdown measures has a stronger effect on accumulated social and economic activity than a continual process of gradual imposing and lifting restrictions on that activity. Third, a scenario of a rapidly imposed severe lockdown has the most drastic consequences for the economy, causing both the sharpest drop in production, the longest time of remaining on the path of relatively lowest growth, and the most dramatic expected accumulated decrease in production. Similar conclusions are drawn as to the changes in social utility.

An epidemic and economic growth. A medium-term perspective

The economic impact of communicable diseases (mortality, loss of working days, fear of contagion, etc.) leads to a decrease in the demand for goods and services that affects the internal income and employment. In this paper, we propose the Solow model of economic growth in the presence of a communicable disease. Our goal is to study the effects of Kalecki’s time delay and the latent period on long-term economic growth. To do this, we prove that there are two equilibria (diseasefree equilibrium and endemic equilibrium). Then, we investigate their stability. Additionally, we show that the endemic equilibrium can be destabilized through a Hopf bifurcation if the latent period cross some critical value. Finally, we give some numerical simulations to illustrate our results.

/pdf/fluctuations-of-solow-economic-growth-model-in-the-presence-3dxidpsott.pdf

Fluctuations of Solow economic growth model in the presence of an infectious disease

In this paper, we propose a mathematical study of the relationship between population dynamics and economic growth. To do this, the total population is divided into three disjoint classes: employed, unemployed and economically inactive population. On the one hand, the evolution of the number of individuals in each compartment is described by Verhulst model and on the other hand the economic growth is governed by the Solow equation. The resulting model is a system of differential equations with time delay. The dynamics, of this system, are studied in terms of local stability and of local Hopf bifurcation. Some numerical simulations are given to illustrate our theoretical results. Additionally we conclude with some remarks.

/pdf/hopf-bifurcation-in-a-delayed-solow-verhulst-model-2zx0q3w2xf.pdf

Hopf Bifurcation in a Delayed Solow-Verhulst Model

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Fluctuations of Solow economic growth model in the presence of an infectious disease

Hopf Bifurcation in a Delayed Solow-Verhulst Model