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 R 0. 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.
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.
Introduction: Often, interns remain unaware of what is expected of them during internship period and work without a clear aim. Induction is a very important process but in reality in many of the medical colleges, internship induction programme is limited to mere 'Hippocratic Oath taking ceremony' for the interns. In this context the present study conducted with the objectives -To evaluate interns 'Gain in learning' through Internship Induction Program (IIP), to assess the perception of interns regarding benefits to them through IIP, to assess perception of faculty members, administrators involved in IIP regarding benefits to interns and to beneficiaries (patients) in hospital/community and to take the feedback from interns, faculties involved, about the newly launched module for IIP. Methods: Study participants were the Interns undergoing IIP(n 1 =166) and the faculty from varied disciplines who participated in IIP(n 2 =20). Study tool were the Pre & post test questionnaire for interns and feedback proforma with regard to IIP & newly launched 'IIP Module', both for interns and faculties. Evaluation has done as per the guidelines of Kirkpatrick's model of programme evaluation where in first two levels of evaluation were considered. Results: Response rate was 100%. Mean Pre-test and post test scores were 6.92±2.55 and 15.03±2.92 respectively (p value<0.05). Absolute learning gain=40.55%, Learning effectiveness score=117%, Class average normalized gain=61%, Effect size=2.95. In feedback analysis for most of the parameters, the rating average was to the right side of the neutral indicating a positive feedback. Conclusion: Programme Evaluation of IIP with Kirkpatrick's model revealed it to be successful in achieving its objective of improving knowledge and attitude of interns.
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