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.

N-Step-Ahead Optimal Control of a Compartmental Model of COVID-19

This paper uses a compartmental model that accounts for some of the main features of the COVID-19 pandemic. Assuming a control that represents the aggregated intensity of non pharmaceutical interventions, such as lockdown in varying degrees and the use of masks and social distancing, this text proposes an N-step-ahead optimal control (NSAOC) method that is easy to calculate and provides a guideline for implementation. The compartmental model is extended to account for vaccination, and the N-step-ahead optimal control is calculated for this case as well. The proposed control is robust to parameter variation in all model parameters, when they are assumed to be normally distributed about nominal values. In addition, the proposed NSAOC is shown to compare favorably with a recently proposed PID-like controller. © 2023, Brazilian Society for Automatics--SBA.

Model-Based Optimization of Vaccination Strategies in Different Phases of Pandemic Virus Spread

This paper aims at applying optimal control principles to investigate optimal vaccination strategies in different phases of a pandemic. Background of the study is that many countries have started their vaccination procedures against the COVID-19 disease in the beginning of 2021, but supply shortages for the vaccines prevented that everyone could be vaccinated immediately. At the beginning of 2022, in contrast, the vaccine supply was ample, but the effectiveness of different existing vaccines to avoid infection by new virus variants was in doubt, as well as the acceptance of booster doses decreased over time. To account for these effects, two formulations of optimization tasks based on different epidemic models are proposed in this paper. The solution of these tasks determines optimal distribution strategies for available vaccines, and optimized vaccination schemes to reduce the need of booster doses for later phase. Effectiveness of these strategies compared with other popular strategies (as applied in practice) is demonstrated through a series of simulations © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID-19 Pandemic with Optimal Control

In this study, a nonlinear deterministic mathematical model that evaluates two important therapeutic measures of the COVID-19 pandemic: vaccination of susceptible and treatment for infected people who are in quarantine, is formulated and rigorously analyzed. Some of the fundamental properties of the model system including existence and uniqueness, positivity, and invariant region of solutions are proved under a certain meaningful set. The model exhibits two equilibrium points: disease-free and endemic equilibrium points under certain conditions. The basic reproduction number, R0, is derived via the next-generation matrix approach, and the dynamical behavior of the model is explored in detail. The analytical analysis reveals that the disease-free equilibrium solution is locally as well as globally asymptotically stable when the associated basic reproduction number is less than unity which indicates that COVID-19 dies out in the population. Also, the endemic equilibrium point is globally asymptotically stable whenever the associated basic reproduction number exceeds a unity which implies that COVID-19 establishes itself in the population. The sensitivity analysis of the basic reproduction number is computed to identify the most dominant parameters for the spreading out as well as control of infection and should be targeted by intervention strategies. Furthermore, we extended the considered model to optimal control problem system by introducing two time-dependent variables that represent the educational campaign to susceptibles and continuous treatment for quarantined individuals. Finally, some numerical results are illustrated to supplement the analytical results of the model using MATLAB ode45. © 2023 Alemzewde Ayalew et al.

How big of an impact do asymptomatic people have on the dynamics of an epidemic?

Asymptomatic carriers serve as a potential source of transmission of epidemic diseases. Exposed people who develop symptoms only get tested and remain isolated in their homes or sometimes in hospitals when needed. In contrast, the asymptomatic individuals go untested and spread the disease silently as they roam freely throughout their entire infectious lifetime. The work intends to explore the role of asymptomatic carriers in the transmission of epidemic diseases and investigate suitable optimal control strategies. We propose a SEIAQR compartmental model subdividing the total population into six different compartments. To illustrate the model's implication, we estimate the number of asymptomatic individuals using COVID-19 data during June 9–July 18, 2021 from Bangladesh. We then analyze the model to explore whether the epidemic subsides if the asymptomatic individuals are tested randomly and isolated. Finally, to gain a better understanding of the potential of this unidentified transmission route, we propose an optimal control model considering two different control strategies: personal protective measures and isolation of asymptomatic carriers through random testing. Our results show that simultaneous implementation of both control strategies can reduce the epidemic early. Most importantly, sustained effort in identifying and isolation of asymptotic individuals allows relaxation in personal protective measures. © 2023

Interacting With COVID-19: How Population Behavior, Feedback and Memory Shaped Recurrent Waves of the Epidemic

Until the approval of vaccines at the end of 2020, societies relied on non-pharmaceutical interventions (NPIs) in order to control the COVID-19 pandemic. Spontaneous changes in individual behavior might have contributed to or counteracted epidemic control due to NPIs. For example, the population compliance to NPIs may have varied over time as people developed 'epidemic fatigue' or altered their perception of the risk and severity of COVID-19. Whereas official measures are well documented, the behavioral response of the citizens is harder to capture. We propose a mathematical model of the societal response, taking into account three main effects: the citizen response dynamics, the authorities' NPIs, and the occurrence of unpreventable events that significantly alter the virus transmission rate. A key assumption is that a society has a waning memory of the epidemic effects, which reflects on both the severity of the authorities' NPIs and on the citizens' compliance to the prescribed rules. This, in turn, feeds back onto the transmission rate of the disease, such that a higher number of hospitalizations decreases the probability of transmission. We show that the model is able to reproduce the COVID-19 dynamics in terms of hospital admissions for several European countries during 2020 over surprisingly long time scales. Also, it is capable of capturing the effects of disturbances (for example the emergence of new virus variants) and can be exploited for implementing control actions to limit such effects. A possible application, illustrated in this letter, consists of exploiting the estimations based on the data of one country, to predict and control the evolution in another country, where the virus spreading is still in an earlier phase. © 2017 IEEE.

Cost-effectiveness of a mathematical modeling with optimal control approach of spread of COVID-19 pandemic: A case study in Peru

COVID-19 pandemic affects 213 countries and regions around the world. Which the number of people infected with the virus exceeded 26 millions infected and more than 870 thousand deaths until september 04, 2020, in the world, and Peru among the countries most affected by this pandemic. So we proposed a mathematical model describes the dynamics of spread of the COVID-19 pandemic in Peru. The optimal control strategy based on the model is proposed, and several reasonable and suitable control strategies are suggested to the prevention and reduce the spread COVID-19 virus, by conducting awareness campaigns and quarantine with treatment. coronavirus 2019 (COVID-19). Pontryagin's maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using Matlab. © 2022

Theoretical analysis of a measles model with nonlinear incidence functions

Measles is a highly contagious respiratory disease of global public health concern. A deterministic mathematical model for the transmission dynamics of measles in a population with Crowley–Martin incidence function to account for the inhibitory effect due to susceptible and infected individuals and vaccination is formulated and analyzed using standard dynamical systems methods. The basic reproduction number is computed. By constructing a suitable Lyapunov function, the disease-free equilibrium is shown to be globally asymptotically stable. Using the Center Manifold theory, the model exhibits a forward bifurcation, which implies that the endemic equilibrium is also globally asymptotically stable. To determine the optimal choice of intervention measures to mitigate the spread of the disease, an optimal control problem is formulated (by introducing a set of three time-dependent control variables representing the first and second vaccine doses, and the palliative treatment) and analyzed using Pontryagin's Maximum Principle. To account for the scarcity of measles vaccines during a major outbreak or other causes such as the COVID-19 pandemic, a Holling type-II incidence function is introduced at the model simulation stage. The control strategies have a positive population level impact on the evolution of the disease dynamics. Graphical results reveal that when the mass-action incidence function is used, the number of individuals who received first and second vaccine dose is smaller compared to the numbers when the Crowley–Martin incidence-type function is used. Inhibitory effect of susceptibles tends to have the same effect on the population level as the Crowley–Martin incidence function, while the control profiles when inhibitory effect of the infectives is considered have similar effect as when the mass-action incidence is used, or when there is limitation in the availability of measles vaccines. Missing out the second measles vaccine dose has a negative impact on the initial disease prevalence. © 2022 Elsevier B.V.

Optimizing Vaccine Allocation Strategies in Pandemic Outbreaks: An Optimal Control Approach

Since early 2020, the world has been dealing with a raging pandemic outbreak: COVID-19. A year later, vaccines have become accessible, but in limited quantities, so that governments needed to devise a strategy to decide which part of the population to prioritize when assigning the available doses, and how to manage the interval between doses for multi-dose vaccines. In this paper, we present an optimization framework to address the dynamic double-dose vaccine allocation problem whereby the available vaccine doses must be administered to different age-groups to minimize specific societal objectives. In particular, we first identify an age-dependent Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model including an extension capturing partially and fully vaccinated people, whereby we account for age-dependent immunity and infectiousness levels together with disease severity. Second, we leverage our model to frame the dynamic age-dependent vaccine allocation problem for different societal objectives, such as the minimization of infections or fatalities, and solve it with nonlinear programming techniques. Finally, we carry out a numerical case study with real-world data from The Netherlands. Our results show how different societal objectives can significantly alter the optimal vaccine allocation strategy. For instance, we find that minimizing the overall number of infections results in delaying second doses, whilst to minimize fatalities it is important to fully vaccinate the elderly first. © 2022 EUCA.

Transmission Dynamics and Optimal Control Strategy to Mitigate the Spread of Novel Coronavirus: The Case of Iran

The outbreak of the novel coronavirus (COVID-19) is currently considered a great challenge to the health of human society. In this study, since the COVID-19 vaccines are currently being developed, a vaccine allocation as an effective pharmaceutical strategy to immunize people against disease is being considered. To this end, a new extended SIR-type model including vaccination compartment and reinfection transmission to predict disease behavior in Iran has been formulated. The mathematical analysis of the model is investigated to verify that the proposed model is well-posed epidemiologically. The biological parameters are evaluated via a nonlinear least-square fitting approach. Finally, to investigate the impact of preventive pharmaceutical measures on flattening the curve of the COVID-19 incidence in Iran, the optimal control strategy is applied. The results of numerical simulations and the optimal control analysis illustrate that the combined implementation of time-dependent measures has a drastic impact on disease burden reduction. © 2022 IEEE.

A state dependent switching optimal control as a formalization of political interventions

The worldwide emergency of the COVID-19 pandemic has shown how the social and economic behaviours, with impact on everyday life of citizens, play a crucial role on the speed and the intensity of the epidemic spread as well as the sanitary effort required for containing the number of hospitalised patients and the mortality rate. Political decisions assumed by the Governments to regulate, moderate and limit the individual contacts were the only effective approach until vaccination started to be massively available. Contacts limitations are always considered, in any Country, as an individual freedom limitation and then it has been seen as an unpopular approach. In this paper, starting from an ad-hoc designed simplified model, an optimal control based approach is used to show how the vaccination rate can effectively contribute to relax the individual limitations. A state based switching technique is adopted to replicate the Governments' decisions based on the epidemic evolution. Some numerical simulations are reported to support the results. © 2022 IEEE.

‘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

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.

A DISTRIBUTED OPTIMAL CONTROL MODEL APPLIED to COVID-19 PANDEMIC

In this paper, a distributed optimal control epidemiological model is presented. The model describes the dynamics of an epidemic with social distancing as a control policy. The model belongs to the class of continuous-time models, usually involving ordinary/partial differential equations, but has a novel feature. The core model-a single integral equation-does not explicitly use transition rates between compartments. Instead, it is based on statistical information on the disease status of infected individuals, depending on the time since infection. The approach is especially relevant for the coronavirus disease 2019 (COVID-19) in which infected individuals are infectious before onset of symptoms during a relatively long incubation period. Based on the analysis of the proposed optimal control problem, including necessary optimality conditions, this paper outlines some efficient numerical approaches. Numerical solutions show some interesting features of the optimal policy for social distancing, depending on the weights attributed to the number of isolated individuals with symptoms and to economic losses due to the enforcement of the control policy. The general nature of the model allows for inclusion of additional epidemic features with minor adaptations in the basic equations. Therefore, the modeling approach may contribute to the analysis of combined intervention strategies and to the guidance of public health decisions. © 2022 Society for Industrial and Applied Mathematics

A Stochastic Model with Optimal Control Strategy of the Transmission of Covid-19

In this work, a stochastic differential equation model about the novel Coronavirus 2019 (COVID-19) is introduced to describe the transmission dynamics of that disease among the susceptible person. By taking the social distance, musk wearing, and other human behavior as a control strategy and introducing an objective function which both considers the limitation of social distance and minimizes the infection population, an optimal control strategy is given numerically. This result gives a new numerical method to simulate the epidemic model and make a new insight into the control strategy choice of the pandemic control under the environments and conditions of different countries. © 2021 IEEE.

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.

An Approximate Numerical Methods for Mathematical and Physical Studies for Covid-19 Models

The advancement in numerical models of serious resistant illnesses is a key research territory in different fields including the nature and the study of disease transmission. One of the aims of these models is to comprehend the elements of conduction of these infections. For the new strain of Covid-19 (Coronavirus), there has been no immunization to protect individuals from the virus and to forestall its spread so far. All things being equal, control procedures related to medical services, for example, social distancing or separation, isolation, and travel limitations can be adjusted to control this pandemic. This article reveals some insights into the dynamic practices of nonlinear Coronavirus models dependent on the homotopy annoyance strategy (HPM). We summon a novel sign stream chart that is utilized to depict the Coronavirus model. Through the numerical investigations, it is uncovered that social separation of the possibly tainted people who might be conveying the infection and the healthy virus-free people can diminish or interrupt the spread of the infection. The mathematical simulation results are highly concurrent with the statistical forecasts. The free balance and dependability focus for the Coronavirus model is discussed and the presence of a consistently steady arrangement is demonstrated. © 2022 CRL Publishing. All rights reserved.