Effect of an antiviral drug control and its variable order fractional network in host COVID-19 kinetics

Abstract

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.

Timely and effective media coverage's role in the spread of Corona Virus Disease 2019

“…We assume that the duration of the outbreak is short enough so that the total number of susceptible persons remains relatively unchanged, and natural deaths and births are ignored 35 . At the same time, because the sum of Equations (–) is zero, the system Equations (–) can be simplified to the following system: The disease‐free equilibrium of system () is For system (), the next generation matrix method 36–39 is used to solve the basic regeneration number . Note that , so , where …”

“…For system (7), the next generation matrix method [36][37][38][39] is used to solve the basic regeneration number R 0 . Note that…”

Application of variable-order fractional calculus in neural networks: where do we stand?

“…In [12], backstepping techniques with constant and variable-order derivatives have been used to develop a synchronization scheme for two identical onescroll systems. In [28], a new variable-order fractional model has been proposed to investigate the effect of antiviral treatment over viral mutation to control disease transmission. Through the genetic algorithm, optimal treatment is presented, and its numerical simulations are illustrated.…”

Global Dynamics of SARS-CoV-2 Infection with Antibody Response and the Impact of Impulsive Drug Therapy

“…The infection processes of SARS-CoV-2, SARS-CoV, and MERS-CoV are similar. Researchers are still working on inter-host modeling for SARS-CoV-2 and target cell limitations under immune responses [31,32]. Hernandez et al [31] proposed a model to examine cellular level dynamics and T cell responses against viral replication.…”

“…Hernandez et al [31] proposed a model to examine cellular level dynamics and T cell responses against viral replication. Wang et al [32] evaluated the effect of several potential interventions for SARS-CoV-2. Their study reveals that combining antiviral drugs with interferons effectively reduces the viral plateau phase and shortens the recovery time.…”