Optimal COVID-19 epidemic control until vaccine deployment

Ramses Djidjou-Demasse; Yannis Michalakis; Marc Choisy; Micea T. Sofonea; Samuel Alizon

The first integral corresponds to the total number of deaths over the time period considered and the second represents the total cost associated with the implementation of the control measures. As earlier studies [14, 17] , we assumed a quadratic expression in the second term associated to the control to capture non-linear costs potentially arising for intense control implementations. When the objective function is quadratic with respect to the control, differential equations arising from optimization have a known solution. Other functional forms often lead to systems of differential equations that are difficult to solve [15] . Finally, B is a coefficient allowing to weight the "cost" associated to the control implementation (c(t)) relative to the cost due to deaths. Our aim is to find the function c * satisfying