As the current COVID-19 outbreak shows, disease epidemic is a complex problem which must be tackled with the right public policy. One of the main tools of the policymakers is to control the contact rate among the population , commonly referred to as social distancing , in order to reduce the spread of the disease. We pose a mean-field game model of individuals each choosing a dynamic strategy of making contacts, given the trade-off of utility from contacts but also risk of infection from those contacts. We compute and compare the mean-field equilibrium (MFE) strategy, which assumes individuals acting selfishly to maximize their own utility, to the socially optimal strategy, which is the strategy maximizing the total utility of the population. We prove that the infected always want to make more contacts than the level at which it would be socially optimal, which reinforces the need to reduce contacts of the infected (e.g. quarantining, sick paid leave). Additionally, we compute the socially optimal strategies, given the costs to incentivize people to change from their selfish strategies . We find that if we impose limited resources, curbing contacts of the infected is more important after the peak of the epidemic has passed. Lastly, we compute the price of anarchy  of this system, to understand the conditions under which large discrepancies between the MFE and socially optimal strategies arise, which is when  public policy would be most effective.
The current COVID-19 pandemic has proven that proper control and prevention of infectious disease require creating and enforcing the appropriate public policies. One critical policy imposed by the policymakers is encouraging the population to practice social distancing (i.e. controlling the contact rate among the population). Here we pose a mean-field game model of individuals each choosing a dynamic strategy of making contacts, given the trade-off of gaining utility but also risking infection from additional contacts. We compute and compare the mean-field equilibrium (MFE) strategy, which assumes each individual acting selfishly to maximize its own utility, to the socially optimal strategy, which maximizes the total utility of the population. We prove that the optimal decision of the infected is always to make more contacts than the level at which it would be socially optimal, which reinforces the important role of public policy to reduce contacts of the infected (e.g. quarantining, sick paid leave). Additionally, we include cost to incentivize people to change strategies, when computing the socially optimal strategies . We find that with this cost, policies reducing contacts of the infected should be further enforced after the peak of the epidemic has passed. Lastly, we compute the price of anarchy (PoA) of this system, to understand the conditions under which large discrepancies between the MFE and socially optimal strategies arise, which is when intervening public policy would be most effective.
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outbreak shows, disease epidemic is a complex problem which must be tackled with the right public policy. One of the main tools of the policymakers is to control the contact rate among the population , commonly referred to as social distancing , in order to reduce the spread of the disease. We
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