ABSTRACT
We formulate an optimal control problem to find best vaccination and treatment policies to minimize the impact of an epidemic on the population. Epidemic spread on heterogeneous human contact networks is modeled using the degree based compartmental model for susceptible-infected-recovered epidemic. Our formulation allows us to study the impact of varying network heterogeneity on the mitigation strategies. Network heterogeneity is varied by using different degree distributions for the network, such as, power law, power law with exponential cut-off, and Poisson. Network heterogeneity is a proxy for social distancing measures applied on the population - as restrictions tightens, high degree hubs disappear, thus, the nature of degree distribution changes from power law to Poisson. We find that high degree nodes assume less importance in mitigating epidemics as the network heterogeneity decreases. Also, epidemics are easier to control with decrease in network heterogeneity. © 2022 IEEE.
ABSTRACT
We formulate an optimal control problem to determine the lockdown policy to curb an epidemic where other control measures are not available yet. We present a unified framework to model the epidemic and economy that allows us to study the effect of lockdown on both of them together. The objective function considers cost of deaths and infections during the epidemic, as well as economic losses due to reduced interactions due to lockdown. We tune the parameters of our model for Covid-19 epidemic and the economies of Burundi, India, and the United States (the low, medium and high income countries). We study the optimal lockdown policies and effect of system parameters for all of these countries. Our framework and results are useful for policymakers to design optimal lockdown strategies that account for both epidemic related infections and deaths, and economic losses due to lockdown. © 2022 IEEE.