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We consider the control of the COVID-19 pandemic through a standard SIR compartmental model. This control is induced by the aggregation of individuals decisions to limit their social interactions: when the epidemic is ongoing, an individual can diminish his/her contact rate in order to avoid getting infected, but this effort comes at a social cost. If each individual lowers his/her contact rate, the epidemic vanishes faster, but the effort cost may be high. A Mean Field Nash equilibrium at the population level is formed, resulting in a lower effective transmission rate of the virus. We prove theoretically that equilibrium exists and compute it numerically. However, this equilibrium selects a sub-optimal solution in comparison to the societal optimum (a centralized decision respected fully by all individuals), meaning that the cost of anarchy is strictly positive. We provide numerical examples and a sensitivity analysis, as well as an extension to a SEIR compartmental model to account for the relatively long latent phase of the COVID-19 disease. In all the scenarii considered, the divergence between the individual and societal strategies happens both before the peak of the epidemic, due to individuals fears, and after, when a significant propagation is still underway.
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Here, we focus on the data analysis of the growth of epidemic spread of Covid-19 in countries where different policies of containment were activated. It is known that the growth of pandemic spread at its threshold is exponential, but it is not known how to quantify the success of different containment policies. We identify that a successful approach gives an arrested phase regime following the Ostwald growth, where, over the course of time, one phase transforms into another metastable phase with a similar free energy as observed in oxygen interstitial diffusion in quantum complex matter and in crystallization of proteins. We introduce the s factor which provides a quantitative measure of the efficiency and speed of the adopted containment policy, which is very helpful not only to monitor the Covid-19 pandemic spread but also for other countries to choose the best containment policy. The results show that a policy based on joint confinement, targeted tests, and tracking positive cases is the most rapid pandemic containment policy; in fact, we found values of 9, 5, and 31 for the success s factor for China, South Korea, and Italy, respectively, where the lowest s factor indicates the best containment policy
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected individuals. For a given social distancing individual strategies, we establish the epidemic reproduction number $R_0$ which can be used to identify network vulnerability and inform vaccination policies. In the second part of the paper we study the equilibrium of the social distancing game, in which individuals choose their social distancing level according to an anticipated global infection rate, which then must equal the actual infection rate following their choices. We give conditions for the existence and uniqueness of equilibrium. For the case of random regular graphs, we show that voluntary social distancing will always be socially sub-optimal.
Mumbai, amongst the most densely populated cities in the world, has witnessed the fourth largest number of cases and the largest number of deaths among all the cities in India (as of 28th October 2020). Along with the rest of India, lockdowns (of varying degrees) have been in effect in Mumbai since March 25, 2020. Given the large economic toll on the country from the lockdown and the related restrictions on mobility of people and goods, swift opening of the economy especially in a financial hub such as Mumbai becomes critical. In this report, we use the IISc-TIFR agent based simulator to develop long term projections for Mumbai under realistic scenarios related to Mumbais opening of the workplaces, or equivalently, the economy, and the associated public transportation through local trains and buses. These projections were developed taking into account a possible second wave if the economy and the local trains are fully opened either on November 1, 2020 or on January 1, 2021. The impact on infection spread in Mumbai if the schools and colleges open on January first week 2021 is also considered. We also try to account for the increased intermingling amongst the population during the Ganeshotsav festival as well as around the Navratri/Dussehra and Diwali festival. Our conclusion, based on our simulations, is that the impact of fully opening up the economy on November 1 is manageable provided reasonable medical infrastructure is in place. Further, schools and colleges opening in January do not lead to excessive increase in infections. The report also explores the relative effectiveness of contact tracing vs containment zones, and also includes very rudimentary results of the effect of vaccinating the elderly population in February 2021.
In response to the COVID-19 pandemic, National governments have applied lockdown restrictions to reduce the infection rate. We perform a massive analysis on near real-time Italian data provided by Facebook to investigate how lockdown strategies affect economic conditions of individuals and local governments. We model the change in mobility as an exogenous shock similar to a natural disaster. We identify two ways through which mobility restrictions affect Italian citizens. First, we find that the impact of lockdown is stronger in municipalities with higher fiscal capacity. Second, we find a segregation effect, since mobility restrictions are stronger in municipalities for which inequality is higher and where individuals have lower income per capita.
The Covid-19 pandemic is ongoing worldwide, and the damage it has caused is unprecedented. For prevention, South Korea has adopted a local quarantine strategy rather than a global lockdown. This approach not only minimizes economic damage, but it also efficiently prevents the spread of the disease. In this work, the spread of COVID-19 under local quarantine measures is modeled using the Susceptible-Exposed-Infected-Recovered model on complex networks. In this network approach, the links connected to isolated people are disconnected and then reinstated when they are released. This link dynamics leads to time-dependent reproduction number. Numerical simulations are performed on networks with reaction rates estimated from empirical data. The temporal pattern of the cumulative number of confirmed cases is then reproduced. The results show that a large number of asymptomatic infected patients are detected as they are quarantined together with infected patients. Additionally, possible consequences of the breakdowns of local quarantine measures and social distancing are considered.
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