SARS-CoV-2 infection with lytic and non-lytic immune responses: A fractional order optimal control theoretical study

Chatterjee, Amar Nath; Basir, Fahad Al; Almuqrin, Muqrin A.; Mondal, Jayanta; Khan, Ilyas

doi:10.1016/j.rinp.2021.104260

Cited by 45 publications

(26 citation statements)

References 24 publications

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“…Fitting data in the early stage of infection under given trade‐offs can determine the range of coefficients involved in the study and make the study in line with the actual situation and convincing. Moreover, if the infection dynamics of SARS‐CoV‐2 within the individuals 54 , 55 , 56 , 57 can be further involved in the present framework instead of “virulence‐transmission” trade‐off hypothesis, a more accurate prediction on the real‐time changes of the virus virulence and the evolutionary scenarios caused by the mutations under such embedded model will be offered. Meanwhile, the micro‐level study on the heterogeneity in host immunity to SARS‐CoV‐2 as well as the possible multiple infections and limited cross‐immunity of the virus might bring the evolutionary diversity of SARS‐CoV‐2.…”

Section: Conclusion and Outlooksmentioning

confidence: 99%

Study on the virulence evolution of SARS‐CoV‐2 and the trend of the epidemics of COVID‐19

Wang

Jiang

2022

Math Methods in App Sciences

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This is the first attempt to investigate the effects of the factors related to non‐pharmaceutical interventions (NPIs) and the physical condition of the public on virulence evolution of SARS‐CoV‐2 and the trend of the epidemics of COVID‐19 under an adaptive dynamics framework. Qualitative agreement of the prediction on the epidemics of COVID‐19 with the actual situations convinced the rationality of the present model. The study showed that enhancing both NPIs (including public vigilance, quarantine measures, and hospitalization) and the physical condition of the public (including susceptibility and recovery speed) contributed to decreasing the prevalence of COVID‐19 but only increasing public vigilance and decreasing the susceptibility of the public could also reduce the virulence of SARS‐CoV‐2. Therefore, controlling the contact rate and infection rate was the key to control not only the epidemic scale of COVID‐19 but also the extent of its harm. On the other hand, the best way to control the epidemics was to increase the public vigilance and physical condition because both of them could reduce the prevalence and case fatality rate (CFR) of COVID‐19. In addition, the enhancement of quarantine measures and hospitalization could bring the (slight) increase in the CFR of COVID‐19.

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Section: Conclusion and Outlooksmentioning

confidence: 99%

Study on the virulence evolution of SARS‐CoV‐2 and the trend of the epidemics of COVID‐19

Wang

Jiang

2022

Math Methods in App Sciences

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“…To study the COVID-19 dynamics within human host, a few mathematical models have been developed [ 2 , 20 – 24 ]. The major target area of the SARS-CoV-2 virus are the epithelial cells in the upper respiratory tract and upper divisions of bronchi [ 2 , 25 ].…”

Section: Introductionmentioning

confidence: 99%

“…They also study the effect of the combination of antiviral drug therapy and its effect on the model dynamics. Chatterjee et al [ 24 ] proposed a group of fractional equations model considering uninfected epithelial cells, infected epithelial cells, SARS-CoV-2 virus, and CTL response inducing cells accounting both the lytic and non-lytic effects of immune response and the effects of commonly used antiviral drugs.…”

Section: Introductionmentioning

confidence: 99%

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

Wanga

Mondal

Samui

et al. 2022

Eur. Phys. J. Spec. Top.

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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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“…Chatterjee and Basir [ 13 ] formulated a mathematical model to examine the consequences of adaptive immune response to the viral mutation in controlling disease transmission and the effect of the combined antiviral drug therapy on the model dynamics. Chatterjee et al [ 34 , 35 ] proposed a set of fractional differential equations model in cellular level accounting the lytic and non-lytic effects of immune response in the kinetics of the model exploring the effect of a commonly used antiviral drug in COVID-19 treatment along applying an optimal control-theoretic approach.…”

Section: Introductionmentioning

confidence: 99%

Dynamical demeanour of SARS-CoV-2 virus undergoing immune response mechanism in COVID-19 pandemic

Mondal

Samui

Chatterjee

2022

Eur. Phys. J. Spec. Top.

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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.

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SARS-CoV-2 infection with lytic and non-lytic immune responses: A fractional order optimal control theoretical study

Cited by 45 publications

References 24 publications

Study on the virulence evolution of SARS‐CoV‐2 and the trend of the epidemics of COVID‐19

Study on the virulence evolution of SARS‐CoV‐2 and the trend of the epidemics of COVID‐19

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

Dynamical demeanour of SARS-CoV-2 virus undergoing immune response mechanism in COVID-19 pandemic

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