scholarly journals Controlling the Spread of COVID-19: Optimal Control Analysis

2020 ◽  
Author(s):  
Chinwendu E. Madubueze ◽  
Sambo Dachollom ◽  
Isaac Obiajulu Onwubuya
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Public Health Education ◽  
Time Dependent ◽  
World Health ◽  
Critical Parameters ◽  
Control Analysis ◽  
Invariant Region ◽  
Control Approach ◽  
Health Organization

AbstractCoronavirus disease 2019 (COVID-19) is a disease caused by Severe acute respiratory syndrome coronavirus 2 (SARS CoV-2). It was declared on March 11, 2020, by the World Health Organization as pandemic disease. The disease has neither approved medicine nor vaccine and has made government and scholars search for drastic measures in combating the pandemic. Regrettably, the spread of the virus and mortality due to COVID-19 has continued to increase daily. Hence, it is imperative to control the spread of the disease particularly using non-pharmacological strategies such as quarantine, isolation and public health education. This work studied the effect of these different control strategies as time-dependent interventions using mathematical modeling and optimal control approach to ascertain their contributions in the dynamic transmission of COVID-19. The model was proven to have an invariant region and was well-posed. The basic reproduction number was computed with and without interventions and was used to carry out the sensitivity analysis that identified the critical parameters contributing to the spread of COVID-19. The optimal control analysis was carried out using the Pontryagin’s maximum principle to figure out the optimal strategy necessary to curtail the disease. The findings of the optimal control analysis and numerical simulations revealed that time-dependent interventions reduced the number of exposed and infected individuals compared to time-independent interventions. These interventions were time-bound and best implemented within the first 100 days of the outbreak. Again, the combined implementation of only two of these interventions produced a good result in reducing infection in the population, while the combined implementation of all three interventions performed better, even though zero infection was not achieved in the population. This implied that multiple interventions need to be deployed early in order to the virus to the barest minimum.

scholarly journals Controlling the Spread of COVID-19: Optimal Control Analysis

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Chinwendu E. Madubueze ◽  
Sambo Dachollom ◽  
Isaac Obiajulu Onwubuya
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Public Health Education ◽  
Time Dependent ◽  
World Health ◽  
Critical Parameters ◽  
Control Analysis ◽  
Invariant Region ◽  
Control Approach ◽  
Health Organization

Coronavirus disease 2019 (COVID-19) is a disease caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV-2). It was declared on March 11, 2020, by the World Health Organization as pandemic disease. The disease has neither approved medicine nor vaccine and has made governments and scholars search for drastic measures in combating the pandemic. Regrettably, the spread of the virus and mortality due to COVID-19 has continued to increase daily. Hence, it is imperative to control the spread of the disease particularly using nonpharmacological strategies such as quarantine, isolation, and public health education. This work studied the effect of these different control strategies as time-dependent interventions using mathematical modeling and optimal control approach to ascertain their contributions in the dynamic transmission of COVID-19. The model was proven to have an invariant region and was well-posed. The basic reproduction number and effective reproduction numbers were computed with and without interventions, respectively, and were used to carry out the sensitivity analysis that identified the critical parameters contributing to the spread of COVID-19. The optimal control analysis was carried out using the Pontryagin’s maximum principle to figure out the optimal strategy necessary to curtail the disease. The findings of the optimal control analysis and numerical simulations revealed that time-dependent interventions reduced the number of exposed and infected individuals compared to time-independent interventions. These interventions were time-bound and best implemented within the first 100 days of the outbreak. Again, the combined implementation of only two of these interventions produced a good result in reducing infection in the population. While, the combined implementation of all three interventions performed better, even though zero infection was not achieved in the population. This implied that multiple interventions need to be deployed early in order to reduce the virus to the barest minimum.

scholarly journals Deterministic Epidemic Models for Ebola Infection with Time-Dependent Controls

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Eric Okyere ◽  
Johnson De-Graft Ankamah ◽  
Anthony Kodzo Hunkpe ◽  
Dorcas Mensah
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Ebola Virus ◽  
Virus Disease ◽  
Control Strategies ◽  
Hamiltonian Function ◽  
Epidemic Models ◽  
Adjoint Equations ◽  
Time Dependent ◽  
Control Analysis

In this paper, we have studied epidemiological models for Ebola infection using nonlinear ordinary differential equations and optimal control theory. We considered optimal control analysis of SIR and SEIR models for the deadly Ebola infection using vaccination, treatment, and educational campaign as time-dependent control functions. We have applied indirect methods to study existing deterministic optimal control epidemic models for Ebola virus disease. These methods in optimal control are based on Hamiltonian function and Pontryagin’s maximum principle to construct adjoint equations and optimality systems. The forward-backward sweep numerical scheme with the fourth-order Runge–Kutta method is used to solve the optimality system for the various control strategies. From our numerical illustrations, we can conclude that effective educational campaigns and vaccination of susceptible individuals as well as effective treatments of infected individuals can help reduce the disease transmission.

scholarly journals Discrete-time inverse optimal control for a reaction wheel pendulum: a passivity-based control approach

2020 ◽  
Vol 19 (4) ◽  
pp. 123-132 ◽  
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Federico Martin Serra
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Point Of View ◽  
Control Analysis ◽  
Inverse Optimal Control ◽  
Reaction Wheel ◽  
Control Approach ◽  
Control Functions ◽  
Passivity Based Control ◽  
The Time Domain

In this paper it is presented the design of a controller for a reaction wheel pendulum using a discrete-time representation via optimal control from the point of view of passivity-based control analysis. The main advantage of the proposed approach is that it allows to guarantee asymptotic stability convergence using a quadratic candidate Lyapunovfunction. Numerical simulations show that the proposed inverse optimal control design permits to reach superiornumerical performance reported by continuous approaches such as Lyapunov control functions and interconnection,and damping assignment passivity-based controllers. An additional advantageof the proposed inverse optimal controlmethod is its easy implementation since it does not employ additional states. It is only required a basic discretizationof the time-domain dynamical model based on the backward representation. All the simulations are carried out inMATLAB/OCTAVE software using a codification on the script environment.

scholarly journals No Evidence of SARS-CoV-2 Circulation in Rome (Italy) during the Pre-Pandemic Period: Results of a Retrospective Surveillance

2020 ◽  
Vol 17 (22) ◽  
pp. 8461
Author(s):  
Carlo Capalbo ◽  
Enrico Bertamino ◽  
Alessandro Zerbetto ◽  
Iolanda Santino ◽  
Andrea Petrucca ◽  
...  
Keyword(s):  
Control Strategies ◽  
Local Level ◽  
Central Italy ◽  
Total Sample ◽  
World Health ◽  
Infection Prevalence ◽  
Health Authorities ◽  
Causative Agents ◽  
Definition Of ◽  
Health Organization

In March 2020, the World Health Organization (WHO) declared that the COVID-19 outbreak recorded over the previous months could be characterized as a pandemic. The first known Italian SARS-CoV-2 positive case was reported on 21 February. In some countries, cases of suspected “COVID-19-like pneumonia” had been reported earlier than those officially accepted by health authorities. This has led many investigators to check preserved biological or environmental samples to see whether the virus was detectable on dates prior to those officially stated. With regard to Italy, the results of a microbiological screening in sewage samples collected between the end of February and the beginning of April 2020 from wastewaters in Milan (Northern Italy) and Rome (Central Italy) showed presence of SARS-CoV-2. In the present study, we evaluated, by means of a standardized diagnostic method, the SARS-CoV-2 infection prevalence amongst patients affected by severe acute respiratory syndrome (SARI) in an academic hospital located in Central Italy during the period of 1 November 2019–1 March 2020. Overall, the number of emergency room (ER) visits during the investigated period was 13,843. Of these, 1208 had an influenza-like syndrome, but only 166 matched the definition of SARI as stated in the study protocol. A total of 52 SARI cases were laboratory confirmed as influenza: 26 as a type B virus, 25 as a type A, and 1 as both viruses. Although about 17% of the total sample had laboratory or radiological data compatible with COVID-19, all the nasopharyngeal swabs stored underwent SARS-CoV-2 RT-PCR and tested negative. Based on our result, it is confirmed that the COVID-19 pandemic spread did not start prior to the “official” onset in central Italy. Routine monitoring of SARI causative agents at the local level is critical for reporting epidemiologic and etiologic trends that may differ from one country to another and also among different influenza seasons. This has a practical impact on prevention and control strategies.

scholarly journals Modelling and Simulating the Novel Coronavirus with Implications of Asymptomatic Carriers

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Ghassane Benrhmach ◽  
Khalil Namir ◽  
Jamal Bouyaghroumni
Keyword(s):  
Control Strategies ◽  
World Health ◽  
Contact Tracing ◽  
Effective Control ◽  
Public Authorities ◽  
Asymptomatic Carriers ◽  
Social Distancing ◽  
Infected People ◽  
Novel Coronavirus ◽  
Health Organization

The World Health Organization declared that the total number of confirmed cases tested positive for SARS‐CoV‐2, affecting 210 countries, exceeded 3 million on 29 April 2020, with more than 207,973 deaths. In order to end the global COVID‐19 pandemic, public authorities have put in place multiple strategies like testing, contact tracing, and social distancing. Predictive mathematical models for epidemics are fundamental to understand the development of the epidemic and to plan effective control strategies. Some hosts may carry SARS‐CoV‐2 and transmit it to others, yet display no symptoms themselves. We propose applying a model (SELIAHRD) taking in consideration the number of asymptomatic infected people. The SELIAHRD model consists of eight stages: Susceptible, Exposed, Latent, Symptomatic Infected, Asymptomatic Infected, Hospitalized, Recovered, and Dead. The asymptomatic carriers contribute to the spread of disease, but go largely undetected and can therefore undermine efforts to control transmission. The simulation of possible scenarios of the implementation of social distancing shows that if we rigorously follow the social distancing rule then the healthcare system will not be overloaded.

A multi-delay model for pest control with awareness induced interventions — Hopf bifurcation and optimal control analysis

2020 ◽  
Vol 13 (06) ◽  
pp. 2050047
Author(s):  
Fahad Al Basir
Keyword(s):  
Optimal Control ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Time Delays ◽  
Control Strategies ◽  
Control Analysis ◽  
Agricultural Practice ◽  
Delay Model ◽  
Awareness Campaigns ◽  
Farming Awareness

Farming awareness is an important measure for pest controlling in agricultural practice. Time delay in controlling pest may affect the system. Time delay occurs in organizing awareness campaigns, also time delay may takes place in becoming aware of the control strategies or implementing suitable controlling methods informed through social media. Thus we have derived a mathematical model incorporating two time delays into the system and Holling type-II functional response. The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays. Stability changes occur through Hopf-bifurcation when time delays cross the critical values. Optimal control theory has been applied for cost-effectiveness of the delayed system. Numerical simulations are carried out to justify the analytical results. This study shows that optimal farming awareness through radio, TV etc. can control the delay induced bifurcation in a cost-effective way.

scholarly journals Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Amira Rachah ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Ebola Virus ◽  
World Health ◽  
Multiple Shooting ◽  
Multiple Shooting Method ◽  
Major Outbreak ◽  
Health Organization ◽  
Spread Of Infection ◽  
The Impact

The Ebola virus is currently one of the most virulent pathogens for humans. The latest major outbreak occurred in Guinea, Sierra Leone, and Liberia in 2014. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multiple shooting method.

scholarly journals Fasciolosis

2011 ◽  
Author(s):  
Michael Parkinson ◽  
John P. Dalton ◽  
Sandra M. O’Neill
Keyword(s):  
At Risk ◽  
Large Scale ◽  
Fasciola Hepatica ◽  
Control Strategies ◽  
Epidemiological Studies ◽  
World Health ◽  
Complex Life Cycle ◽  
Human Populations ◽  
Specific Stage ◽  
Health Organization

Liver fluke disease, or fasciolosis, of livestock and humans is caused by endoparasitic trematodes of the genus Fasciola. Fasciola hepatica is responsible for the disease in temperate climates whereas F. gigantica is found in tropical zones. Recently, hybrids between F. hepatica and F. gigantica have been described (Le et al. 2008, Periago et al. 2008). Fasciolosis is a true zoonoses as it is predominantly a disease of animals that can be transmitted to humans at a specific stage of the parasite’s complex life cycle. There are a number of definitive hosts which includes sheep, cattle, and humans but this parasite has evolved to infect many other mammalian hosts including pigs, dogs, alpacas, llamas, rats, and goats (Apt et al. 1993; Chen and Mott 1990; Esteban et al. 1998). While prevalence of infection in humans may be relatively low in relation to animals, in specific geographic locations, for example in Bolivia, the prevalence of fasciolosis is so high in the human populations (hyperendemic) that it contributes to the spread of disease in animals (Esteban et al. 1999; Mas-Coma et al. 1999).Archeological studies showing Fasciola eggs in ancient mummies in Egypt demonstrate that fasciolosis is an ancient human disease (David 1997). Sporadic cases of fasciolosis were reported in Egypt in 1958 (Kuntz et al. 1958). The first to carry out an extensive review on human fasciolosis were Chen and Mott (1990). They reported 2,595 cases in over 40 countries in Europe, the Americas, Asia, Africa and the western Pacifi c from 1970 – 1990. This review raised awareness of fasciolosis in humans and triggered a growth in epidemiological studies and a consequential dramatic increase in reporting of cases in the literature. Now human fasciolosis is recognized by the World Health Organization (WHO) as an important disease in humans with an estimated 2.4 million people infected annually and 180 million at risk to infection in over 61 countries (Haseeb et al. 2002). There have been several cases of large scale epidemics in France (Dauchy et al. 2007), Egypt (Curtale et al. 2007) and Iran (Rokni et al. 2002).However, the only extensive epidemiological studies to determine the rate of infection have been carried out in Egypt and Bolivia (Curtale et al. 2003, 2007; Esteban et al. 2002; Parkinson et al. 2007). These studies have shown that co-infection with other diseases is a common occurrence and this may lead to under-reporting of the incidence of fasciolosis (Esteban et al. 2003; Maiga et al. 1991). In many countries, the overall rates of infection are extrapolated from sporadic reports of the disease and, consequently, worldwide disease prevalence is uncertain. In this chapter we will review the cause and effect of human fasciolosis, and particularly highlight important considerations in designing control strategies to reduce infection in at-risk communities.

scholarly journals Mathematical Modeling and Optimal Control Analysis of COVID-19 in Ethiopia

2020 ◽  
Author(s):  
Haileyesus Tessema Alemneh ◽  
Getachew Teshome Telahun
Keyword(s):  
Optimal Control ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Control Model ◽  
Control Analysis ◽  
Basic Model ◽  
Short Period ◽  
Disease Free

In this paper we developed a deterministic mathematical model of the pandemic COVID-19 transmission in Ethiopia, which allows transmission by exposed humans. We proposed an SEIR model using system of ordinary differential equations. First the major qualitative analysis, like the disease free equilibruim point, endemic equilibruim point, basic reproduction number, stability analysis of equilibrium points and sensitivity analysis was rigorously analysed. Second, we introduced time dependent controls to the basic model and extended to an optimal control model of the disease. We then analysed using Pontryagins Maximum Principle to derive necessary conditions for the optimal control of the pandemic. The numerical simulation indicated that, an integrated strategy effective in controling the epidemic and the gvernment must apply all control strategies in combating COVID-19 at short period of time.

scholarly journals Transmission Dynamics of Hepatitis C with Control Strategies

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Adnan Khan ◽  
Sultan Sial ◽  
Mudassar Imran
Keyword(s):  
Optimal Control ◽  
Hepatitis C ◽  
Deterministic Model ◽  
Control Strategies ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Critical Parameters ◽  
Optimal Controls ◽  
Infected Population ◽  
The Impact

We present a rigorous mathematical analysis of a deterministic model, for the transmission dynamics of hepatitis C, using a standard incidence function. The infected population is divided into three distinct compartments featuring two distinct infection stages (acute and chronic) along with an isolation compartment. It is shown that for basic reproduction number R0≤1, the disease-free equilibrium is locally and globally asymptotically stable. The model also has an endemic equilibrium for R0>1. Uncertainty and sensitivity analyses are carried out to identify and study the impact of critical parameters on R0. In addition, we have presented the numerical simulations to investigate the influence of different important parameters on R0. Since we have a locally stable endemic equilibrium, optimal control is applied to the deterministic model to reduce the total infected population. Two different optimal control strategies (vaccination and isolation) are designed to control the disease and reduce the infected population. Pontryagin’s Maximum Principle is used to characterize the optimal controls in terms of an optimality system which is solved numerically. Numerical results for the optimal controls are compared against the constant controls and their effectiveness is discussed.

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