Highlights We propose a SAIU compartmental mathematical model that explains the transmission dynamics of COVID-19. Perform local and global stability analysis for the infection free and endemic equilibrium point. A sensitivity analysis is conducted to identify the most effective parameters with respect to basic reproduction number R 0 .

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

COVID-19 is caused by the increase of SARS-CoV-2 viral load in the respiratory system. Epithelial cells in the human lower respiratory tract are the major target area of the SARS-CoV-2 viruses. To fight against the SARS-CoV-2 viral infection, innate and thereafter adaptive immune responses be activated which are stimulated by the infected epithelial cells. Strong immune response against the COVID-19 infection can lead to longer recovery time and less severe secondary complications. We proposed a target cell-limited mathematical model by considering a saturation term for SARS-CoV-2-infected epithelial cells loss reliant on infected cells level. The analytical findings reveal the conditions for which the system undergoes transcritical bifurcation and alternation of stability for the system around the steady states happens. Due to some external factors, while the viral reproduction rate exceeds its certain critical value, backward bifurcation and reinfection may take place and to inhibit these complicated epidemic states, host immune response, or immunopathology would play the essential role. Numerical simulation has been performed in support of the analytical findings.

In December 2019, a novel coronavirus disease (COVID-19) appeared in Wuhan, China. After that, it spread rapidly all over the world. Novel coronavirus belongs to the family of Coronaviridae and this new strain is called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epithelial cells of our throat and lungs are the main target area of the SARS-CoV-2 virus which leads to COVID-19 disease. In this article, we propose a mathematical model for examining the effects of antiviral treatment over viral mutation to control disease transmission. We have considered here three populations namely uninfected epithelial cells, infected epithelial cells, and SARS-CoV-2 virus. To explore the model in light of the optimal control-theoretic strategy, we use Pontryagin’s maximum principle. We also illustrate the existence of the optimal control and the effectiveness of the optimal control is studied here. Cost-effectiveness and efficiency analysis confirms that time-dependent antiviral controlled drug therapy can reduce the viral load and infection process at a low cost. Numerical simulations have been done to illustrate our analytical findings. In addition, a new variable-order fractional model is proposed to investigate the effect of antiviral treatment over viral mutation to control disease transmission. Considering the superiority of fractional order calculus in the modeling of systems and processes, the proposed variable-order fractional model can provide more accurate insight for the modeling of the disease. Then through the genetic algorithm, optimal treatment is presented, and its numerical simulations are illustrated.

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