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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.

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.

This article consists of a detailed and novel stochastic optimal control analysis of a coupled non-linear dynamical system. The state equations are modelled as an additional food-provided prey–predator system with Holling type III functional response for predator and intra-specific competition among predators. We first discuss the optimal control problem as a Lagrangian problem with a linear quadratic control. Second, we consider an optimal control problem in the time-optimal control setting. We initially establish the existence of optimal controls for both these problems and later characterize these optimal controls using the Stochastic maximum principle. Further numerical simulations are performed based on stochastic forward-backward sweep methods for realizing the theoretical findings. The results obtained in these optimal control problems are discussed in the context of biological conservation and pest management.

In this study, we have formulated and analyzed a non-linear compartmental model (SEIR) for the dynamics of COVID-19 with reference to immigration from urban to rural population in Indian scenario. We have captured the effect of the immigration as two separate factors contributing in the rural compartments of the model. We have first established the positivity of the solution and the boundedness of the solution followed by the existence and uniqueness of the solution for this multi compartment model. We later went on to find out the equibria of the system and derived the reproduction number. Further we numerically depicted the local and global stability of the equilibria. Later we have done sensitivity analysis of the model parameters and identified the sensitive parameters of the system. The sensitivity analysis is followed up with the two parameter heat plots dealing with the sensitive parameters of the system. These heat plots gives us the parameter regions in which the system is stable. Finally comparative and effectiveness studies were done with reference to the control interventions such as Vaccination, Antiviral drugs, Immunotheraphy.