Epidemic Control: Social Distancing or Antiviral Medications?

In this study, we investigate different control scenarios through theoretical analysis and numerical simulations. To account for two important types of control for an early ascending stage of an outbreak, social distancing and treatment with antiviral medications, a compartmental model is considered with one control, $u_1(t)$, aimed to lower the disease transmission rate and the other control, $u_2(t)$, aimed to lower the period of infectiousness. In all experiments, the implementation of control strategies reduces the daily cumulative number of cases and successfully "flattens the curve". The reduction in the cumulative cases is achieved by eliminating or delaying new cases. This delay is incredibly valuable as it provides public health organizations with more time to advance antiviral treatments and devise alternative preventive measures. The main theoretical result of the paper, Theorem 3.1, concludes that the optimal control functions, $u_i(t)$, $i=1,2,$ may be increasing until some moment $\tau \in [0, T)$. However, for all $t \in [\tau, T]$, both controls, $u_i(t)$, decline as $t$ approaches $T$ (possibly causing the number of newly infected people to grow). Numerical simulations presented in Section 4 confirm theoretical findings, which indicates that, ideally, around the time $t=\tau$, the control strategy has to be upgraded and a vaccination campaign needs to start to ensure the epidemic wave does not rebound.