SIR economic epidemiological models with disease induced mortality

Abstract

This paper studies an optimal growth model where there is an infectious disease with SIR dynamics which can lead to mortality. Health expenditures (alternatively intensity of lockdowns) can be made to reduce infectivity of the disease. We study implications of two different ways to model the disease related mortality -early and late in infection mortality -on the equilibrium health and economic outcomes. In the former, increasing mortality reduces infections by decreasing the fraction of infectives in the population, while in the latter the fraction of infectives increases. We characterize the steady states and the outcomes depend in the way mortality is modeled. With early mortality, increasing mortality leads to higher equilibrium per capita output and consumption while in the late mortality model these decrease. We establish sufficiency conditions and provide the first results in economic models with SIR dynamics with and without disease related mortality -a class of models which are non-convex and have endogenous discounting so that no existing results are applicable.

COVID-19 and a Green Recovery?

“…Then l inherits the dynamics of l = 1 − i . 8 We are assuming for simplicity that all infected workers do not work (see Goenka and Liu, 2020 , and Goenka, et al, 2021a , for further discussion of this assumption).…”

“… 6 Goenka, et al, 2020b , modeled mortality in an SIS model, Goenka, et al, 2021a , in an SIR model and Goenka, et al, 2021b , in an SIRS model. All of these did not consider the role of pollution.…”

“… 12 The sufficiency conditions have been extended to account for mortality in Goenka, et al, 2020b , and for the SIR model with mortality in Goenka, et al, 2021a , and SIRS model with mortality in Goenka, et al, 2021b . …”

An Epidemic Compartment Model for Economic Policy Directions for Managing Future Pandemic

“…Epidemic models and their interactions with the economy was studied in [8,15,5] More recently, SIR model, disease-related mortality and effect on economy was studied in [10].…”

“…Under assumptions(1)(2)(3)(4)(5)(6)(7)(8)(9)(10) , for each fixed b ∈ [µ,(1−p) β −γ) if θ > θmax (b), then A * = 0, e * = 0, * h = 0, m * = 0, k * = k, l * = l, c * = f (k, l) − δ K + b − µ kis the unique steady state solution to the system given in Equations (4.14-4.24). In otherwords, when θ > θmax there exist unique endemic steady state without health expenditure and without direct investment to control the epidemic.Proof.…”