Optimal interventions of infectious disease

The recent outbreak of novel coronavirus has highlighted the need for a benefit-cost framework to guide unconventional public health interventions aimed at reducing close contact between infected and susceptible individuals. In this paper, we propose an optimal control problem for an infectious disease model, wherein the social planner can control the transmission rate by implementing or lifting lockdown measures. The objective is to minimize total costs, which comprise infection costs, as well as fixed and variable costs associated with lockdown measures. We establish conditions concerning model primitives that guarantee the existence of a straightforward optimal policy. The policy specifies two switching points (Formula presented.), whereby the social planner institutes a lockdown when the percentage of infected individuals exceeds (Formula presented.), and reopens the economy when the percentage of infected individuals drops below (Formula presented.). We subsequently extend the model to cases where the social planner may implement multiple lockdown levels. Finally, numerical studies are conducted to gain additional insights into the value of these controls. © 2023 Wiley Periodicals LLC.

Optimal Capacity-Constrained COVID-19 Vaccination for Heterogeneous Populations

COVID-19 and the ensuing vaccine capacity constraints have emphasized the importance of proper prioritization during vaccine rollout. This problem is complicated by heterogeneity in risk levels, contact rates, and network topology which can dramatically and unintuitively change the efficacy of vaccination and must be taken into account when allocating resources. This paper proposes a general model to capture a wide array of network heterogeneity while maintaining computational tractability and formulates vaccine prioritization as an optimal control problem. Pontryagin's Maximum Principle is used to derive properties of optimal, potentially highly dynamic, allocation policies, providing significant reductions in the set of candidate policies. Extensive numerical simulations of COVID-19 vaccination are used to corroborate these findings and further illicit optimal policy characteristics and the effects of various system, disease, and population parameters. © 2022 IEEE.

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 COVID-19 epidemic strategy with vaccination control and infection prevention measures in Thailand.

COVID-19 is a severe acute respiratory syndrome caused by the Coronavirus-2 virus (SARS-CoV-2). The virus spreads from one to another through droplets from an infected person, and sometimes these droplets can contaminate surfaces that may be another infection pathway. In this study, we developed a COVID-19 model based on data and observations in Thailand. The country has strictly distributed masks, vaccination, and social distancing measures to control the disease. Hence, we have classified the susceptible individuals into two classes: one who follows the measures and another who does not take the control guidelines seriously. We conduct epidemic and endemic analyses and represent the threshold dynamics characterized by the basic reproduction number. We have examined the parameter values used in our model using the mean general interval (GI). From the calculation, the value is 5.5 days which is the optimal value of the COVID-19 model. Besides, we have formulated an optimal control problem to seek guidelines maintaining the spread of COVID-19. Our simulations suggest that high-risk groups with no precaution to prevent the disease (maybe due to lack of budgets or equipment) are crucial to getting vaccinated to reduce the number of infections. The results also indicate that preventive measures are the keys to controlling the disease.

‘Period doubling’ induced by optimal control in a behavioral SIR epidemic model

We consider a behavioral SIR epidemic model to describe the action of the public health system aimed at enhancing the social distancing during an epidemic outbreak. An optimal control problem is proposed where the control acts in a specific way on the contact rate. We show that the optimal control of social distancing is able to generate a period doubling–like phenomenon. Namely, the ‘period’ of the prevalence is the double of the ‘period’ of the control, and an alternation of small and large peaks of disease prevalence can be observed. © 2022 Elsevier Ltd

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.

Impact of Network Heterogeneity on Epidemic Mitigation Strategies

We formulate an optimal control problem to find best vaccination and treatment policies to minimize the impact of an epidemic on the population. Epidemic spread on heterogeneous human contact networks is modeled using the degree based compartmental model for susceptible-infected-recovered epidemic. Our formulation allows us to study the impact of varying network heterogeneity on the mitigation strategies. Network heterogeneity is varied by using different degree distributions for the network, such as, power law, power law with exponential cut-off, and Poisson. Network heterogeneity is a proxy for social distancing measures applied on the population - as restrictions tightens, high degree hubs disappear, thus, the nature of degree distribution changes from power law to Poisson. We find that high degree nodes assume less importance in mitigating epidemics as the network heterogeneity decreases. Also, epidemics are easier to control with decrease in network heterogeneity. © 2022 IEEE.

Mathematical optimization modeling for estimating the incidence of clinical diseases

The notion that infectious disease transmission and dissemination are governed by rules that may be expressed mathematically is not new. In fact, the nonlinear dynamics of infectious illness transmission were only fully recognized in the twentieth century. However, with the Coronavirus outbreak, there is a lot of discussion and study regarding the origin of the epidemic and how it spreads before all vulnerable people are infected, as well as ideas about how the disease virulence changes during the epidemic. In this paper, we provide some critical mathematical models which are SIR and SIS and their differences in approach for the interpretation and transmission of viruses and other epidemics as well as formulate the optimal control problem with vaccinations.

Optimal Lockdown to Manage an Epidemic

We formulate an optimal control problem to determine the lockdown policy to curb an epidemic where other control measures are not available yet. We present a unified framework to model the epidemic and economy that allows us to study the effect of lockdown on both of them together. The objective function considers cost of deaths and infections during the epidemic, as well as economic losses due to reduced interactions due to lockdown. We tune the parameters of our model for Covid-19 epidemic and the economies of Burundi, India, and the United States (the low, medium and high income countries). We study the optimal lockdown policies and effect of system parameters for all of these countries. Our framework and results are useful for policymakers to design optimal lockdown strategies that account for both epidemic related infections and deaths, and economic losses due to lockdown. © 2022 IEEE.

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.

The effectiveness of contact tracing in mitigating COVID-19 outbreak: A model-based analysis in the context of India.

The ongoing pandemic situation due to COVID-19 originated from the Wuhan city, China affects the world in an unprecedented scale. Unavailability of totally effective vaccination and proper treatment regimen forces to employ a non-pharmaceutical way of disease mitigation. The world is in desperate demand of useful control intervention to combat the deadly virus. This manuscript introduces a new mathematical model that addresses two different diagnosis efforts and isolation of confirmed cases. The basic reproductive number, R 0 , is inspected, and the model's dynamical characteristics are also studied. We found that with the condition R 0 < 1 , the disease can be eliminated from the system. Further, we fit our proposed model system with cumulative confirmed cases of six Indian states, namely, Maharashtra, Tamil Nadu, Andhra Pradesh, Karnataka, Delhi and West Bengal. Sensitivity analysis carried out to scale the impact of different parameters in determining the size of the epidemic threshold of R 0 . It reveals that unidentified symptomatic cases result in an underestimation of R 0 whereas, diagnosis based on new contact made by confirmed cases can gradually reduce the size of R 0 and hence helps to mitigate the ongoing disease. An optimal control problem is framed using a control variable u ( t ) , projecting the effectiveness of diagnosis based on traced contacts made by a confirmed COVID patient. It is noticed that optimal contact tracing effort reduces R 0 effectively over time.

Determination of an optimal control strategy for vaccine administration in COVID-19 pandemic treatment.

BACKGROUND AND OBJECTIVE: For decades, mathematical models have been used to predict the behavior of physical and biological systems, as well as to define strategies aiming at the minimization of the effects regarding different types of diseases. In the present days, the development of mathematical models to simulate the dynamic behavior of the novel coronavirus disease (COVID-19) is considered an important theme due to the quantity of infected people worldwide. In this work, the objective is to determine an optimal control strategy for vaccine administration in COVID-19 pandemic treatment considering real data from China. Two optimal control problems (mono- and multi-objective) to determine a strategy for vaccine administration in COVID-19 pandemic treatment are proposed. The first consists of minimizing the quantity of infected individuals during the treatment. The second considers minimizing together the quantity of infected individuals and the prescribed vaccine concentration during the treatment. METHODS: An inverse problem is formulated and solved in order to determine the parameters of the compartmental Susceptible-Infectious-Removed model. The solutions for both optimal control problems proposed are obtained by using Differential Evolution and Multi-objective Optimization Differential Evolution algorithms. RESULTS: A comparative analysis on the influence related to the inclusion of a control strategy in the population subject to the epidemic is carried out, in terms of the compartmental model and its control parameters. The results regarding the proposed optimal control problems provide information from which an optimal strategy for vaccine administration can be defined. CONCLUSIONS: The solution of the optimal control problem can provide information about the effect of vaccination of a population in the face of an epidemic, as well as essential elements for decision making in the economic and governmental spheres.