ABSTRACT
In this study, we develop a mathematical model incorporating age-specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the positivity and boundedness of the solutions of the non controlled model and calculate the basic reproduction number and do the stability analysis. We then formulate an optimal control problem with vaccination and treatment as control variables and study the same. Pontryagin's Minimum Principle is used to obtain the optimal vaccination and treatment rates. Optimal vaccination and treatment policies are analysed for different values of the weight constant associated with the cost of vaccination and different efficacy levels of vaccine. Findings from these suggested that the combined strategies (vaccination and treatment) worked best in minimizing the infection and disease induced mortality. In order to reduce COVID-19 infection and COVID-19 induced deaths to maximum, it was observed that optimal control strategy should be prioritized to the population with age greater than 40 years. Varying the cost of vaccination it was found that sufficient implementation of vaccines (more than 77 %) reduces the size of COVID-19 infections and number of deaths. The infection curves varying the efficacies of the vaccines against infection were also analysed and it was found that higher efficacy of the vaccine resulted in lesser number of infections and COVID induced deaths. The findings would help policymakers to plan effective strategies to contain the size of the COVID-19 pandemic. © 2022 Bishal Chhetri et al., published by De Gruyter.
ABSTRACT
The pandemic COVID-19 is an infectious respiratory illness caused by SARS CoV-2 (severe acute respiratory syndrome coronavirus-2) and it spreads human-to-human. Due to the COVID-19 outbreak, the world is facing an unprecedented loss of lives around the globe and highlighted an effective treatment to deal with the virus. Natural products have historically been utilized for respiratory disease and display promising toxicity. Natural products have been reported for several antiviral activities of viruses, like influenza, HIV and some coronaviruses SARS-CoV and MERS-CoV. Therefore, natural products could be a vital resource for developing efficient and safe antiviral drugs against COVID-19. This review summarized the inhibition of isolated compounds from medicinal plants against different coronaviruses which could lead to the development of effective antiviral drugs to counter COVID-19. © 2022, Rasayan Journal of Chemistry, c/o Dr. Pratima Sharma. All rights reserved.
ABSTRACT
COVID-19 pandemic has resulted in more than 257 million infections and 5.15 million deaths worldwide. Several drug interventions targeting multiple stages of the pathogenesis of COVID-19 can significantly reduce induced infection and thus mortality. In this study, we first develop SIV model at within-host level by incorporating the intercellular time delay and analyzing the stability of equilibrium points. The model dynamics admits a disease-free equilibrium and an infected equilibrium with their stability based on the value of the basic reproduction number R0. We then formulate an optimal control problem with antiviral drugs and second-line drugs as control measures and study their roles in reducing the number of infected cells and viral load. The comparative study conducted in the optimal control problem suggests that if the first-line antiviral drugs show adverse effects, considering these drugs in reduced amounts along with the second-line drugs would be very effective in reducing the number of infected cells and viral load in a COVID-19 infected patient. Later, we formulate a time-optimal control problem with the goal of driving the system from any initial state to the desired infection-free equilibrium state in finite minimal time. Using Pontryagin's Minimum Principle, it is shown that the optimal control strategy is of the bang-bang type, with the possibility of switching between two extreme values of the optimal controls. Numerically, it is shown that the desired infection-free state is achieved in a shorter time when the higher values of the optimal controls. The results of this study may be very helpful to researchers, epidemiologists, clinicians and physicians working in this field. © 2021 Bishal Chhetri et al., published by De Gruyter.
ABSTRACT
The dynamics of COVID-19 in India are captured using a set of delay differential equations by dividing a population into five compartments. The Positivity and Boundedness of the system is shown. The Existence and Uniqueness condition for the solution of system of equations is presented. The equilibrium points are calculated and stability analysis is performed. Sensitivity analysis is performed on the parameters of the model. Bifurcation analysis is performed and the critical delay is calculated. By formulating the spread parameter as a function of temperature, the impact of temperature on the population is studied. We concluded that with the decrease in temperature, the average infections in the population increases. In view of the coming winter season in India, there will be an increase in new infections. This model falls in line with the characteristics that increase in isolation delay increases average infections in the population. © 2021 D Bhanu Prakash et al.
ABSTRACT
The COVID-19 pandemic has resulted in more 176 million cases and around 3.82 million deaths worldwide. Different drug interventions acting at multiple stages of the pathogenesis of COVID-19 can substantially reduce infection-induced mortality. The current within-host mathematical modeling studies deals with the optimal combined drug intervention strategy and its efficacy in reducing the burden of COVID-19. The drug interventions considered here include Hydroxychloroquine (HCQ), the first BCG vaccine dose, and a booster dose of BCG administered at a later stage. In this work, we consider two scenarios involving the administration of these interventions. The findings of these studies include the following: the average infected cell count and viral load decreased the most when both the HCQ and BCG interventions were applied together in both scenarios. On the other hand, the average susceptible cell count decreased the best when HCQ alone was administered in both these scenarios. From the comparative effectiveness study it was observed that the basic reproduction number and viral count decreased the best when HCQ and BCG booster interventions were applied together, reinstating the fact obtained earlier in the optimal control setting. These findings may help physicians with decision making in the treatment of life-threatening COVID-19 pneumonia. This study involving different drug interventions is first of its kind. © Research India Publications.