It still isn't game theory, the government acts first, the voters act after after observing the outcome. There is no subsequent game. It is simply up to the go

It still isn't game theory, the government acts first, the voters act after after observing the outcome. There is no subsequent game. It is simply up to the government to estimate probability and expected payoff. Optimal action for government is to take the least amount of action to prevent the voters from thinking its a pandemic. It isn't a game theory scenario, there are no nash equilibria.