Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies

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.

Optimal Drug Regimen and Combined Drug Therapy and Its Efficacy in the Treatment of COVID-19: A Within-Host Modeling Study.

The COVID-19 pandemic has resulted in more than 524 million cases and 6 million deaths worldwide. Various drug interventions targeting multiple stages of COVID-19 pathogenesis can significantly reduce infection-related mortality. The current within-host mathematical modeling study addresses the optimal drug regimen and efficacy of combination therapies in the treatment of COVID-19. The drugs/interventions considered include Arbidol, Remdesivir, Interferon (INF) and Lopinavir/Ritonavir. It is concluded that these drugs, when administered singly or in combination, reduce the number of infected cells and viral load. Four scenarios dealing with the administration of a single drug, two drugs, three drugs and all four are discussed. In all these scenarios, the optimal drug regimen is proposed based on two methods. In the first method, these medical interventions are modeled as control interventions and a corresponding objective function and optimal control problem are formulated. In this framework, the optimal drug regimen is derived. Later, using the comparative effectiveness method, the optimal drug regimen is derived based on the basic reproduction number and viral load. The average number of infected cells and viral load decreased the most when all four drugs were used together. On the other hand, the average number of susceptible cells decreased the most when Arbidol was administered alone. The basic reproduction number and viral load decreased the most when all four interventions were used together, confirming the previously obtained finding of the optimal control problem. The results of this study can help physicians make decisions about the treatment of the life-threatening COVID-19 infection.

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III.

COVID-19 pandemic has caused the most severe health problems to adults over 60 years of age, with particularly fatal consequences for those over 80. In this case, age-structured mathematical modeling could be useful to determine the spread of the disease and to develop a better control strategy for different age groups. In this study, we first propose an age-structured model considering two different age groups, the first group with population age below 30 years and the second with population age above 30 years, and discuss the stability of the equilibrium points and the sensitivity of the model parameters. In the second part of the study, we propose an optimal control problem to understand the age-specific role of treatment in controlling the spread of COVID -19 infection. From the stability analysis of the equilibrium points, it was found that the infection-free equilibrium point remains locally asymptotically stable when R 0 < 1 , and when R 0 is greater than one, the infected equilibrium point remains locally asymptotically stable. The results of the optimal control study show that infection decreases with the implementation of an optimal treatment strategy, and that a combined treatment strategy considering treatment for both age groups is effective in keeping cumulative infection low in severe epidemics. Cumulative infection was found to increase with increasing saturation in medical treatment.

Time Optimal Control Studies on COVID-19 Incorporating Adverse Events of the Antiviral Drugs

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.

Control Intervention Strategies for Within-Host, Between-Host and their Efficacy in the Treatment, Spread of COVID-19: A Multi Scale Modeling Approach

The COVID-19 pandemic has resulted in more than 65.5 million infections and 15,14,695 deaths in 212 countries over the last few months. Different drug intervention acting at multiple stages of pathogenesis of COVID-19 can substantially reduce the infection induced, thereby decreasing the mortality. Also population level control strategies can reduce the spread of the COVID-19 substantially. Motivated by these observations, in this work we propose and study a multi scale model linking both within-host and between-host dynamics of COVID-19. Initially the natural history dealing with the disease dynamics is studied. Later comparative effectiveness is performed to understand the efficacy of both the within-host and population level interventions. Findings of this study suggest that a combined strategy involving treatment with drugs such as Arbidol, remdesivir, Lopinavir/Ritonavir that inhibits viral replication and immunotherapies like monoclonal antibodies, along with environmental hygiene and generalized social distancing proved to be the best and optimal in reducing the basic reproduction number and environmental spread of the virus at the population level. © 2020 D. Bhanu Prakash et al., published by De Gruyter.

Low temperatures or high isolation delay increases the average COVID-19 infections in India: A Mathematical modeling approach

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.

Combined drug interventions and its efficacy in the reduction of COVID-19 burden: A within-host modeling study with reference to HCQ and BCG vaccination

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.

Within-host mathematical modeling on crucial inflammatory mediators and drug interventions in COVID-19 identifies combination therapy to be most effective and optimal

The unprecedented Covid-19 pandemic has resulted in more than 14.75 million infections and 6, 10, 839 deaths in 212 countries. Appropriate interventions can decrease the rate of Covid-19 related mortality. Fast track clinical trials around the world are addressing the efficacy of individual pharmaceutical agent acting at various stages of pathogenesis. However, lessons learnt while dealing with past viral epidemics mandates, simultaneous use of such drugs in combination amongst different populations. Mathematical modelling studies can be extremely helpful in understanding the efficacy of drugs both individually and in combination. The current within-host mathematical model studies the natural history of Covid-19 in terms of complex interplay of virus replication and behaviour of host immune response. Additionally it studies the role of various drugs at various stages of pathogenesis. The model was validated by generating two-parameter heat plots, representing the characteristics of Covid-19, the sensitivity analysis identified the crucial parameters. The efficacy of interventions was assessed by optimal control problem. The model dynamics exhibited disease-free equilibrium and the infected equilibrium with their stability, based on the reproduction number R0, the transcritical bifurcation observed at R0=1. The burst rate and the natural death rate of the virus were observed as most significant parameters in the life-threatening Covid-19 pneumonia. The antiviral drugs affecting viral replication and those modulating the immune response, reduce the infected cells and viral load significantly. However, the yield was optimal and most effective when the combination therapy involving one or more antiviral and one or more immunomodulating drugs were administered together. These findings may help physicians with early decision making in treatment of life-threatening Covid-19 infection.