Global Properties and Optimal Control Strategies of a Generalized Ebola Virus Disease Model

2021 ◽  
pp. 99-114
Author(s):  
Zineb El Rhoubari ◽  
Hajar Besbassi ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Optimal Control ◽  
Ebola Virus ◽  
Virus Disease ◽  
Control Strategies ◽  
Disease Model ◽  
Ebola Virus Disease ◽  
Global Properties

AN OPTIMAL CONTROL MODEL FOR EBOLA VIRUS DISEASE

2016 ◽  
Vol 24 (01) ◽  
pp. 29-49 ◽  
Author(s):  
SYLVIE DIANE DJIOMBA NJANKOU ◽  
FARAI NYABADZA
Keyword(s):  
Optimal Control ◽  
Ebola Virus ◽  
Virus Disease ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
Case Fatality ◽  
Ebola Virus Disease ◽  
Joint Control ◽  
Transversality Conditions ◽  
Necessary And Sufficient

The most deadly Ebola outbreak in the history, which started in December [Formula: see text], is currently under control. The high case fatality rate of the Ebola outbreak inspired local and international control strategies. In this paper, the dynamics of Ebola virus disease is modeled in the presence of three control strategies. The model describes the evolution of the disease in the population when educational campaigns, active case-finding and pharmaceutical interventions are implemented as control strategies against the disease. We prove the existence of an optimal control set and analyze the necessary and sufficient conditions, optimality and transversality conditions. We conclude through numerical simulations that containing an Ebola outbreak needs early and long-term implementation of joint control strategies.

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.

Modeling transmission dynamics of Ebola virus disease

2017 ◽  
Vol 10 (04) ◽  
pp. 1750057 ◽  
Author(s):  
Mudassar Imran ◽  
Adnan Khan ◽  
Ali R. Ansari ◽  
Syed Touqeer Hussain Shah
Keyword(s):  
Ebola Virus ◽  
Virus Disease ◽  
Control Strategies ◽  
Transmission Dynamics ◽  
Ebola Virus Disease ◽  
Transmission Model ◽  
Globally Asymptotically Stable ◽  
Dynamical Systems Analysis ◽  
Number Formula ◽  
Disease Free

Ebola virus disease (EVD) has emerged as a rapidly spreading potentially fatal disease. Several studies have been performed recently to investigate the dynamics of EVD. In this paper, we study the transmission dynamics of EVD by formulating an SEIR-type transmission model that includes isolated individuals as well as dead individuals that are not yet buried. Dynamical systems analysis of the model is performed, and it is consequently shown that the disease-free steady state is globally asymptotically stable when the basic reproduction number, [Formula: see text] is less than unity. It is also shown that there exists a unique endemic equilibrium when [Formula: see text]. Using optimal control theory, we propose control strategies, which will help to eliminate the Ebola disease. We use data fitting on models, with and without isolation, to estimate the basic reproductive numbers for the 2014 outbreak of EVD in Liberia and Sierra Leone.

scholarly journals Modelling and Optimal Control of Ebola Virus Disease in the Presence of Treatment and Quarantine of Infectives

2020 ◽  
Vol 5 (4) ◽  
pp. 43
Author(s):  
Herick Laiton Kayange ◽  
Estomih Shedrack Massawe ◽  
Daniel Oluwole Makinde ◽  
Lathika Sunil Immanuel
Keyword(s):  
Optimal Control ◽  
Ebola Virus ◽  
Virus Disease ◽  
Ebola Virus Disease

scholarly journals Recurrent outbreaks of Ebola Virus Disease in Africa: A Meta-analysis of case fatality rates

2020 ◽  
Author(s):  
Joseph Kawuki ◽  
Taha Hussein Musa ◽  
Xiaojin Yu
Keyword(s):  
Ebola Virus ◽  
Assessment Tool ◽  
Virus Disease ◽  
Control Strategies ◽  
Meta Analysis ◽  
Case Fatality ◽  
Ebola Virus Disease ◽  
Surveillance Systems ◽  
Potential Factors ◽  
English Articles

Abstract Background: In the last decade, Africa has witnessed several outbreaks of Ebola virus disease (EVD), each presenting with varying case fatality rate (CFR) and other socio-economic impacts. This study aims to summarise the CFR and identify potential factors that influenced the severity of EVD outbreaks in Africa.Methods: This was a systematic review and meta-analysis of EVD outbreaks published between January 2010 and March 2020, using Web of Science, Scopus and PubMed databases. Only English articles and reports, including the number of cases and deaths during the outbreak in Africa, were considered. Quality of the included articles was assessed using the Murad’s quality assessment tool. The analysis was conducted using Stata (version 12), pooled effect sizes were calculated using the random-effects model and heterogeneity was tested for using the I2 statistic.Result: Thirteen studies with 32,300 cases and 13,727 deaths were identified whose pooled CFR was 60% (95% CI: 47-73%). The most EVD-affected countries were DRC with 5 outbreaks and a pooled CFR of 65% (95% CI: 59-71%), followed by Uganda with 3 outbreaks and CFR= 83% (95% CI: 60-99%). Zaire ebolavirus caused the most outbreaks (10), with a CFR= 58% (95% CI: 45-71%). Besides, outbreaks with less than 1000 cases reported a higher CFR rate compared to those with more cases.Conclusion: The study has revealed a considerably high CFR caused by the recurrent EVD outbreaks in Africa. It also notes an implementation gap of the prevention and control strategies, and thus identifies a need to strengthen the surveillance systems and response mechanisms to enable early detection and prompt control of future outbreaks.

Modeling the impact of migrated population on human-to-human transmission of Ebola virus disease

2018 ◽  
Vol 09 (01) ◽  
pp. 1850008
Author(s):  
Abhinav Tandon ◽  
Sankha Banerjee
Keyword(s):  
Ebola Virus ◽  
Virus Disease ◽  
Disease Model ◽  
Critical Values ◽  
Ebola Virus Disease ◽  
Reproductive Number ◽  
Contact Rates ◽  
The Stability ◽  
Time Required ◽  
The Impact

A nonlinear SEIR mathematical model is developed to investigate the impact of migrated population, infected with Ebola virus, on human-to-human transmission of Ebola Virus Disease (EVD) in a disease-free area. In view of the dynamics of Ebola virus disease, here, the infected class is supposed to be divided into subclasses, viz. primary and secondary infected. The proposed model is analyzed qualitatively using the stability theory of differential equations and quantitatively using numerical simulation. The obtained results, qualitatively and quantitatively, suggest that migration and contact rates play an important role in controlling the spreading of disease. Critical values for migration and contact rates are evaluated and it is revealed that if these rates go beyond their critical values, it leads to delay in the stabilization of the system. It is also found that primary reproductive number increases with increase in migration rate. Besides this, the approximate time required to attain stability of the disease model system is also determined. The model analysis recommends quarantining the noninfected from the secondary infected in order to control the spreading out of disease.

scholarly journals Study on modeling simulation and optimal control method for the transmission risk of the Ebola virus

SIMULATION ◽  
2018 ◽  
Vol 95 (3) ◽  
pp. 195-208
Author(s):  
Shihao Liu
Keyword(s):  
Optimal Control ◽  
Equilibrium State ◽  
Ebola Virus ◽  
Control Method ◽  
Virus Disease ◽  
Ebola Virus Disease ◽  
Transmission Risk ◽  
Logistics System ◽  
Optimal Control Method ◽  
Negative Effect

In order to prevent and control the transmission risk of the Ebola virus, an Ebola virus disease SEIQR model was built. The free-Ebola-virus-disease equilibrium state and the Ebola-virus-disease equilibrium state of the SEIQR model are asymptotically stable. On the basis of the SEIQR model, the numerical simulation was formulated. From the simulation curves, it is found that if the production speed of the medicine cannot keep pace with demand, the transmission risk of Ebola will become out of control. Assuming that the medicine demand point and the medicine supply point constitute a logistics system in a certain planar range, the center-of-gravity method was used to obtain the optimal location for medicine delivery. By using this discrete-time virus model’s optimal control rate to control the serious transmission risk of Ebola virus in the crowd, the effective strategy for transmission was added to the model, and then the control sheet was obtained. From the simulation results on the basis of the SEIQR model, it is concluded that the theory of the optimal control rate has a negative effect on the transmission risk of Ebola.

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