The model distinguishes for each of the states (E), (A), (I) and (R) two degrees of severity: severe (s) and "not severe" (or "mild" (m)). The goal of the paper is to find an optimal control c*(t) which minimizes an appropriate cost function; this optimal control is computed by numerically solving a system of optimality obtained using the Pontryagin maximum principle. This optimal strategy consists of a control with an intensity that increases sharply at first and then decreases steadily. The authors show the superiority of this strategy compared to strategies often suggested by epidemiologists, such as the constant control strategy, the so-called lock-down strategy, or also cyclic strategies which consist in alternating minimum and maximum values for the control function. I think that the results obtained will be very useful for epidemiologists.
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