Mathematical modeling of COVID‐19 and Omicron outbreak spread: Optimal control approach for intervention strategies

In Morocco, 966,777 confirmed cases and 14,851 confirmed deaths because of COVID‐19 were recorded as of January 1, 2022. Recently, a new strain of COVID‐19, the so‐called Omicron variant, was reported in Morocco, which is considered to be more dangerous than the existing COVID‐19 virus. To end this ongoing global COVID‐19 pandemic and Omicron variant, there is an urgent need to implement multiple population‐wide policies like vaccination, testing more people, and contact tracing. To forecast the pandemic's progress and put together a strategy to effectively contain it, we propose a new hybrid mathematical model that predicts the dynamics of COVID‐19 in Morocco, considering the difference between COVID‐19 and the Omicron variant, and investigate the impact of some control strategies on their spread. The proposed model monitors the dynamics of eight compartments, namely susceptible (S)$$ (S) $$ , exposed (E)$$ (E) $$ , infected with COVID‐19 (I)$$ (I) $$ , infected with Omicron (IO)$$ \left({I}_O\right) $$ , hospitalized (H)$$ (H) $$ , people in intensive care units (U)$$ (U) $$ , quarantined (Q)$$ (Q) $$ , and recovered (R)$$ (R) $$ , collectively expressed as SEIIOHUQR$$ SEI{I}_O HUQR $$ . We calculate the basic reproduction number ℛ0$$ {\mathcal{R}}_0 $$ , studying the local and global infection‐free equilibrium stability, a sensitivity analysis is conducted to determine the robustness of model predictions to parameter values, and the sensitive parameters are estimated from the real data on the COVID‐19 pandemic in Morocco. We incorporate two control variables that represent vaccination and diagnosis of infected individuals and we propose an optimal strategy for an awareness program that will help to decrease the rate of the virus' spread. Pontryagin's maximum principle is used to characterize the optimal controls, and the optimality system is solved by an iterative method. Finally, extensive numerical simulations are employed with and without controls to illustrate our results using MATLAB software. Our results reveal that achieving a reduction in the contact rate between uninfected and infected individuals by vaccinating and diagnosing the susceptible individuals, can effectively reduce the basic reproduction number and tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended period of time. The model simulations demonstrate that the elimination of the ongoing SARS‐COV‐2 pandemic and its variant Omicron in Morocco is possible by implementing, at the start of the pandemic, a strategy that combines the two variables of control mentioned above. Our predictions are based on real data with reasonable assumptions.