Optimal control strategies of non-pharmaceutical and pharmaceutical interventions for COVID-19 control

In recent, non-pharmaceutical intervention (lockdown, quarantine, expended testing) and the pharmaceutical intervention (use of commonly used drugs) are the only available strategies to control the COVID-19 disease. Though the scientist all over the world are engaging themselves to find the way out the vaccine of COVID-19, still it is persisted unanswered how to oust the pandemic epidemic from the world. Generally, social distancing, using the mask, etc. are the only available policy to control the pandemic. In this situation uses of common drugs (Azithromycin, HCQ, Antiprotozoal with Doxycycline, Levocetirizine with Montelukast) are common but effective treatment for the reported and hospitalized patient. These drugs activate the immune system of our body to fight against the disease progression. We have formulated a seven compartmental SEIQR type model to explore the COVID-19 disease progression. We have studied the effect of pharmaceutical and non pharmaceutical intervention as a control input and it effect to reduce the number of the infected population while reducing the cost related with the awareness and drug in a specific time frame. Analytical finding tells that the system behavior depends on basic reproduction number and awareness related to social distancing, using the mask and common drug usage are proposed to be sustained so that disease can be controlled. Numerical study support our analytical findings.