Managing infectious diseases over connected populations: a non-convex optimal control (original) (raw)
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Optimal control of epidemics in metapopulations
Journal of The Royal Society Interface, 2009
Little is known about how best to deploy scarce resources for disease control when epidemics occur in different but interconnected regions. We use a combination of optimal control methods and epidemiological theory for metapopulations to address this problem. We consider what strategy should be used if the objective is to minimize the discounted number of infected individuals during the course of an epidemic. We show, for a system with two interconnected regions and an epidemic in which infected individuals recover and can be reinfected, that equalizing infection in the two regions is the worst possible strategy in minimizing the total level of infection. Treatment should instead be preferentially directed at the region with the lower level of infection, treating the other subpopulation only when there is resource left over. The same strategy holds with preferential treatments of regions with lower levels of infection when quarantine is introduced.
Resource Allocation for Epidemic Control in Metapopulations
PLoS ONE, 2011
Deployment of limited resources is an issue of major importance for decision-making in crisis events. This is especially true for large-scale outbreaks of infectious diseases. Little is known when it comes to identifying the most efficient way of deploying scarce resources for control when disease outbreaks occur in different but interconnected regions. The policy maker is frequently faced with the challenge of optimizing efficiency (e.g. minimizing the burden of infection) while accounting for social equity (e.g. equal opportunity for infected individuals to access treatment). For a large range of diseases described by a simple SIRS model, we consider strategies that should be used to minimize the discounted number of infected individuals during the course of an epidemic. We show that when faced with the dilemma of choosing between socially equitable and purely efficient strategies, the choice of the control strategy should be informed by key measurable epidemiological factors such as the basic reproductive number and the efficiency of the treatment measure. Our model provides new insights for policy makers in the optimal deployment of limited resources for control in the event of epidemic outbreaks at the landscape scale.
Application of Optimal Control of Infectious Diseases in a Model-Free Scenario
SN Computer Science, 2021
Optimal control for infectious diseases has received increasing attention over the past few decades. In general, a combination of cost state variables and control effort have been applied as cost indices. Many important results have been reported. Nevertheless, it seems that the interpretation of the optimal control law for an epidemic system has received less attention. In this paper, we have applied Pontryagin's maximum principle to develop an optimal control law to minimize the number of infected individuals and the vaccination rate. We have adopted the compartmental model SIR to test our technique. We have shown that the proposed control law can give some insights to develop a control strategy in a model-free scenario. Numerical examples show a reduction of 50% in the number of infected individuals when compared with constant vaccination. There is not always a prior knowledge of the number of susceptible, infected, and recovered individuals required to formulate and solve the optimal control problem. In a model-free scenario, a strategy based on the analytic function is proposed, where prior knowledge of the scenario is not necessary. This insight can also be useful after the development of a vaccine to COVID-19, since it shows that a fast and general cover of vaccine worldwide can minimize the number of infected, and consequently the number of deaths. The considered approach is capable of eradicating the disease faster than a constant vaccination control method.
Journal of Theoretical Biology, 2010
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CoSIR: Managing an Epidemic via Optimal Adaptive Control of Transmission Rate Policy
2020
ABSTRACTShaping an epidemic with an adaptive contact restriction policy that balances the disease and socioeconomic impact has been the holy grail during the COVID-19 pandemic. Most of the existing work on epidemiological models focuses on scenario-based forecasting via simulation but techniques for explicit control of epidemics via an analytical framework are largely missing. In this paper, we consider the problem of determining the optimal control policy for transmission rate assuming SIR dynamics, which is the most widely used epidemiological paradigm. We first demonstrate that the SIR model with infectious patients and susceptible contacts (i.e., product of transmission rate and susceptible population) interpreted as predators and prey respectively reduces to a Lotka-Volterra (LV) predator-prey model. The modified SIR system (LVSIR) has a stable equilibrium point, an “energy” conservation property, and exhibits bounded cyclic behaviour similar to an LV system. This mapping permi...
Disease Spread in Coupled Populations: Minimizing Response Strategies Costs in Discrete Time Models
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Social distancing, vaccination, and medical treatments have been extensively studied and widely used to control the spread of infectious diseases. However, it is still a difficult task for health administrators to determine the optimal combination of these strategies when confronting disease outbreaks with limited resources, especially in the case of interconnected populations, where the flow of individuals is usually restricted with the hope of avoiding further contamination. We consider two coupled populations and examine them independently under two variants of well-known discrete time disease models. In both examples we compute approximations for the control levels necessary to minimize costs and quickly contain outbreaks. The main technique used is simulated annealing, a stochastic search optimization tool that, in contrast with traditional analytical methods, allows easy implementation to any number of patches with different kinds of couplings and internal dynamics.
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Advances in Difference Equations, 2020
The effect of infectious diseases cannot be overemphasised. The continuing surfacing of the infectious diseases gives the stakeholders a great concern. In this paper, the nature of the spread of Ebola virus outbreak in West Africa in 2014 is studied. We develop a model that analyses the spread of infectious diseases, and the reproduction number is determined by using the next generation matrix method. Finally, the effects of treatment of the infected individuals and vaccination of the susceptible population as the control strategies are looked into. The optimal control system showed that the combination of the two strategies proved more effective.
Optimal Vaccination of an Endemic Model with Variable Infectivity and Infinite Delay
Zeitschrift für Naturforschung A, 2013
In this work, we consider a nonlinear SEIR (susceptible, exposed, infectious, and removed) endemic model, which describes the dynamics of the interaction between susceptible and infected individuals in a population. The model represents the disease evolution through a system of nonlinear differential equations with variable infectivity which determines that the infectivity of an infected individual may not be constant during the time after infection. To control the spread of infection and to find a vaccination schedule for an endemic situation, we use optimal control strategies which reduce the susceptible, exposed, and infected individuals and increase the total number of recovered individuals. In order to do this, we introduce the optimal control problem with a suitable control function using an objective functional. We first show the existence of an optimal control for the control problem and then derive the optimality system. Finally the numerical simulations of the model is identified to fit realistic measurement which shows the effectiveness of the model.
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