Optimal COVID-19 epidemic control until vaccine deployment

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

Overall, for our parameter values, the average of the optimal control during the control period is c * ≈ 0.3. In the first stage, the optimal control increases rapidly to an intermediate value of approximately 0.5 (Figure 2a ) and the epidemics remains under control for a long time period during which healthcare capacity is not overwhelmed (Figure 2b) . Consequently, the number of deaths is strictly minimized during this first stage even though the control is far from its highest level (Figure 2c,d) . After this stage during which a dampened epidemic peak is achieved, the number of severe cases starts to decrease (Figure 2d) , and the control intensity is progressively relaxed until the end of the time interval considered (Figure 2a) . Importantly, in the absence of any take-over by health measures such as vaccine, the epidemic will certainly rebounce after the period of control. Indeed, only a small proportion of the population has been exposed (less than 0.03%) at the end of control period, which is far from the 1 − 1/R 0 ≈ 60% required to reach the herd immunity threshold.