Optimal Control for Economic Development During the Pandemic

Studies in Applied Mathematics, 2021

At the time when this paper was written, quarantine-related strategies (from full lockdown to some relaxed preventive measures) were the only available measure to control coronavirus disease 2019 (COVID-19) epidemic. However, long-term quarantine and especially full lockdown is an extremely expensive measure.

IISE Transactions on Healthcare Systems Engineering, 2017

In preparation and response to an influenza pandemic, knowledge of disease spread as well as effective intervention strategies in place are critical to mitigate its impacts. We propose a simulation-based optimization model that minimizes the costs associated with the pandemic occurrence, while capturing how influenza spreads among individuals based on the sociodemographic characteristics of the population. Multiple intervention strategies including school closure and home confinement are considered to incorporate the changes of a pandemic course in our model and to measure the corresponding effects on the number of infected people. In addition, we apply the NSGS (Nelson, Swann, Goldsman, Song) procedure to achieve computationally efficient and tractable solutions to the resulting large-scale problem. Using real data from Jefferson County, Kentucky with a population more than 700,000 obtained from the U.S. Census Bureau, we present computational results to demonstrate the efficacy of applying the proposed approach.

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Mathematical modeling represents a useful instrument to describe epidemic spread and to propose useful control actions, such as vaccination scheduling, quarantine, informative campaign, and therapy, especially in the realistic hypothesis of resources limitations. Moreover, the same representation could efficiently describe different epidemic scenarios, involving, for example, computer viruses spreading in the network. In this paper, a new model describing an infectious disease and a possible complication is proposed; after deep-model analysis discussing the role of the reproduction number, an optimal control problem is formulated and solved to reduce the number of dead patients, minimizing the control effort. The results show the reasonability of the proposed model and the effectiveness of the control action, aiming at an efficient resource allocation; the model also describes the different reactions of a population with respect to an epidemic disease depending on the economic and s...

soaltci.org

Introduced is an Interacting Particle System (IPS) approach to modeling a multiple stage pandemic. The model population receives differing treatments with possibly differing costs depending on the stage of exposure/infection. The total cost of treatment is a time varying utility function of the ensemble population for which this approach uses particle system methods to simulate the cost of maintaining survival of the population. Interacting Particle Systems are a class of spatial-temporal stochastic processes suitable for studying the spread of infectious diseases and other interaction phenomena. The paper gives a brief background on particle systems with specific focus on "the contact process", followed by expanding the contact process to represent more realistic state transitions.

2021

COVID-19 is an infectious disease caused by the SARS-CoV-2 virus, which spreads so fast in the inhabitants. The virus is transmitted through direct contact with respiratory droplets of an infected individuals through coughing and sneezing or indirect contact through contaminated objects or surface. In this article, a non-linear mathematical model is proposed and analyzed to manifest the impact of transmission dynamics of the COVID-19 pandemic based on Indian condition by considering asymptomatic and symptomatic infections. It is assumed that the transmission rates due to asymptomatic and symptomatic individuals are different. The basic reproduction number of the model is computed and studied the stability of different equilibria of the model in detail. The sensitivity analysis is presented to identify the key parameters that influence the basic reproduction number, which can be regulated to control the transmission dynamics of the disease. Also, this model is extended to the optimal...

Journal of Biological Systems, 2007

The quarantine of suspected cases and isolation of individuals with symptoms are two of the primary public health control measures for combating the spread of a communicable emerging or re-emerging disease. Implementing these measures, however, can inflict significant socio-economic and psychological costs. This paper presents a deterministic compartmental model for assessing the single and combined impact of quarantine and isolation to contain an epidemic. Comparisons are made with a mass vaccination program. The model is simulated using parameters for influenza-type diseases such as SARS. The study shows that even for an epidemic in which asymptomatic transmission does not occur, the quarantine of asymptomatically-infected individuals can be more effective than only isolating individuals with symptoms, if the associated reproductive number is high enough. For the case where asymptomatic transmission occurs, it is shown that isolation is more effective for a disease with a small ba...

Globally, the COVID-19 presents a serious concern to the wellbeing of people. COVID-19 was first detected in Wuhan, China. The disease became a source of concern for Nigerians after the country registered its first case in February 2020. Currently, the country has recorded 255,103 confirmed cases, 249,246 recovered cases, and 3,142 deaths as of March 21, 2022. We proposed a SEQIHRV model to investigate the spread of coronavirus disease in Nigeria. This model defines the infection dynamics' transmission routes as well as effect of contaminated surfaces on the human population. Unfortunately, the virus's propagation and mortality from COVID-19 is increasing daily. Therefore, it is required to manage and control the flow of the infection. The impact of control measures as time-dependent interventions was investigated in this study utilizing optimization technique to determine their effects on the spread of Corona virus. The basic reproduction was calculated and used to calcite ...

Proceedings of the Royal Society of London. Series B: Biological Sciences, 2004

Severe acute respiratory syndrome (SARS), a new, highly contagious, viral disease, emerged in China late in 2002 and quickly spread to 32 countries and regions causing in excess of 774 deaths and 8098 infections worldwide. In the absence of a rapid diagnostic test, therapy or vaccine, isolation of individuals diagnosed with SARS and quarantine of individuals feared exposed to SARS virus were used to control the spread of infection. We examine mathematically the impact of isolation and quarantine on the control of SARS during the outbreaks in Toronto, Hong Kong, Singapore and Beijing using a deterministic model that closely mimics the data for cumulative infected cases and SARS-related deaths in the first three regions but not in Beijing until mid-April, when China started to report data more accurately. The results reveal that achieving a reduction in the contact rate between susceptible and diseased individuals by isolating the latter is a critically important strategy that can control SARS outbreaks with or without quarantine. An optimal isolation programme entails timely implementation under stringent hygienic precautions defined by a critical threshold value. Values below this threshold lead to control, but those above are associated with the incidence of new community outbreaks or nosocomial infections, a known cause for the spread of SARS in each region. Allocation of resources to implement optimal isolation is more effective than to implement sub-optimal isolation and quarantine together. A community-wide eradication of SARS is feasible if optimal isolation is combined with a highly effective screening programme at the points of entry.

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.

Scientifica, 2020

A deterministic ordinary differential equation model for SARS-CoV-2 is developed and analysed, taking into account the role of exposed, mildly symptomatic, and severely symptomatic persons in the spread of the disease. It is shown that in the absence of infective immigrants, the model has a locally asymptotically stable disease-free equilibrium whenever the basic reproduction number is below unity. In the absence of immigration of infective persons, the disease can be eradicated whenever ℛ 0 < 1 . Specifically, if the controls u i , i = 1,2,3,4 , are implemented to 100% efficiency, the disease dies away easily. It is shown that border closure (or at least screening) is indispensable in the fight against the spread of SARS-CoV-2. Simulation of optimal control of the model suggests that the most cost-effective strategy to combat SARS-CoV-2 is to reduce contact through use of nose masks and physical distancing.