Mathematical modeling of contact tracing as a control strategy of Ebola virus disease

More than 20 outbreaks of Ebola virus disease have occurred in Africa since 1976, and yet no adequate treatment is available. Hence, prevention, control measures and supportive treatment remain the only means to avoid the disease. Among these measures, contact tracing occupies a prominent place. In this paper, we propose a simple mathematical model that incorporates imperfect contact tracing, quarantine and hospitalization (or isolation). The control reproduction number [Formula: see text] of each sub-model and for the full model are computed. Theoretically, we prove that when [Formula: see text] is less than one, the corresponding model has a unique globally asymptotically stable disease-free equilibrium. Conversely, when [Formula: see text] is greater than one, the disease-free equilibrium becomes unstable and a unique globally asymptotically stable endemic equilibrium arises. Furthermore, we numerically support the analytical results and assess the efficiency of different control strategies. Our main observation is that, to eradicate EVD, the combination of high contact tracing (up to 90%) and effective isolation is better than all other control measures, namely: (1) perfect contact tracing, (2) effective isolation or full hospitalization, (3) combination of medium contact tracing and medium isolation.

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Modeling transmission dynamics of Ebola virus disease

International Journal of Biomathematics ◽

10.1142/s1793524517500577 ◽

2017 ◽

Vol 10 (04) ◽

pp. 1750057 ◽

Cited By ~ 4

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.

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TRANSMISSION DYNAMICS OF EBOLA VIRUS DISEASE WITH VACCINE, CONDOM USE, QUARANTINE, ISOLATION AND TREATMENT DRUG

African Journal of Infectious Diseases ◽

10.21010/ajid.v15i1.2 ◽

2020 ◽

Vol 15 (1) ◽

pp. 10-23

Author(s):

Queeneth Ojoma Ahman ◽

Omale David ◽

Asogwa Christopher Chukwuma ◽

Nnaji Daniel Ugochukwu ◽

Mbah Godwin Christopher Ezike

Keyword(s):

Stability Analysis ◽

Condom Use ◽

Ebola Virus ◽

Virus Disease ◽

Human Life ◽

Control Measures ◽

Ebola Virus Disease ◽

Asymptotically Stable ◽

Short Period ◽

The Stability

Background: Ebola Virus Disease (EVD) has brought the human population, especially the West African race, great losses in so many areas such as economic productivity and human life. During the 2014 Ebola Virus outbreak, the disease devastated and threatened the whole world. EVD symptoms (fever, diarrhea, vomiting, etc) may appear anywhere between two to twenty-one days after infection. Those that recovered from the disease return to being susceptible again and can transmit the virus through semen as research has shown the virus presence in semen even after recovery. Material and Methods: Mathematical modeling method with the combination of vaccine, condom use, quarantine, isolation and treatment drug together as control measures in a population consisting of human and animals. A model system of non-linear differential equations for the control of EVD was formulated and the model effective reproduction number ( ) was obtained using the next generation matrix method and used in the stability analysis of the model. Center manifold theorem was used in the bifurcation analysis of the model. Results: The result shows that the stability analysis of the model shows that the EVD – Free Equilibrium is locally asymptotically stable when and EVD - Endemic Equilibrium is locally asymptotically stable when . The model was shown to exhibit a forward bifurcation. Conclusions: Numerical simulations and analysis of the model show that EVD could be effectively controlled and eradicated within a short period of time when vaccine, condom use, quarantine, isolation and treatment drug control measures are implemented together.

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A MATHEMATICAL MODEL FOR EBOLA EPIDEMIC WITH SELF-PROTECTION MEASURES

Journal of Biological System ◽

10.1142/s0218339018500067 ◽

2018 ◽

Vol 26 (01) ◽

pp. 107-131 ◽

Cited By ~ 4

Author(s):

T. BERGE ◽

M. CHAPWANYA ◽

J. M.-S. LUBUMA ◽

Y. A. TEREFE

Keyword(s):

Mathematical Model ◽

Ebola Virus ◽

Virus Disease ◽

Mass Action ◽

Transmission Dynamics ◽

Asymptotically Stable ◽

Protection Measures ◽

Globally Asymptotically Stable ◽

New Formulation ◽

Self Protection

A mathematical model presented in Berge T, Lubuma JM-S, Moremedi GM, Morris N Shava RK, A simple mathematical model for Ebola in Africa, J Biol Dyn 11(1): 42–74 (2016) for the transmission dynamics of Ebola virus is extended to incorporate vaccination and change of behavior for self-protection of susceptible individuals. In the new setting, it is shown that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number [Formula: see text] is less than or equal to unity and unstable when [Formula: see text]. In the latter case, the model system admits at least one endemic equilibrium point, which is locally asymptotically stable. Using the parameters relevant to the transmission dynamics of the Ebola virus disease, we give sensitivity analysis of the model. We show that the number of infectious individuals is much smaller than that obtained in the absence of any intervention. In the case of the mass action formulation with vaccination and education, we establish that the number of infectious individuals decreases as the intervention efforts increase. In the new formulation, apart from supporting the theory, numerical simulations of a nonstandard finite difference scheme that we have constructed suggests that the results on the decrease of the number of infectious individuals is valid.

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Contact tracing performance during the Ebola virus disease outbreak in Kenema district, Sierra Leone

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2016.0300 ◽

2017 ◽

Vol 372 (1721) ◽

pp. 20160300 ◽

Cited By ~ 8

Author(s):

Mikiko Senga ◽

Alpha Koi ◽

Lina Moses ◽

Nadia Wauquier ◽

Philippe Barboza ◽

...

Keyword(s):

Sierra Leone ◽

Contact Line ◽

Ebola Virus ◽

Virus Disease ◽

The Body ◽

Physical Contact ◽

Ebola Virus Disease ◽

Contact Tracing ◽

Retrospective Data Analysis ◽

Increased Risk

Contact tracing in an Ebola virus disease (EVD) outbreak is the process of identifying individuals who may have been exposed to infected persons with the virus, followed by monitoring for 21 days (the maximum incubation period) from the date of the most recent exposure. The goal is to achieve early detection and isolation of any new cases in order to prevent further transmission. We performed a retrospective data analysis of 261 probable and confirmed EVD cases in the national EVD database and 2525 contacts in the Contact Line Lists in Kenema district, Sierra Leone between 27 April and 4 September 2014 to assess the performance of contact tracing during the initial stage of the outbreak. The completion rate of the 21-day monitoring period was 89% among the 2525 contacts. However, only 44% of the EVD cases had contacts registered in the Contact Line List and 6% of probable or confirmed cases had previously been identified as contacts. Touching the body fluids of the case and having direct physical contact with the body of the case conferred a 9- and 20-fold increased risk of EVD status, respectively. Our findings indicate that incompleteness of contact tracing led to considerable unmonitored transmission in the early months of the epidemic. To improve the performance of early outbreak contact tracing in resource poor settings, our results suggest the need for prioritized contact tracing after careful risk assessment and better alignment of Contact Line Listing with case ascertainment and investigation. This article is part of the themed issue ‘The 2013–2016 West African Ebola epidemic: data, decision-making and disease control’.

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A Mathematical Model for the Control of the Spread of Ebola Virus Disease in West Africa – A Disease-free Equilibrium Approach

British Journal of Mathematics & Computer Science ◽

10.9734/bjmcs/2016/21930 ◽

2016 ◽

Vol 12 (5) ◽

pp. 1-9

Author(s):

A. Kalu ◽

N. Akuagwu ◽

I. Agwu

Keyword(s):

Mathematical Model ◽

West Africa ◽

Ebola Virus ◽

Virus Disease ◽

Ebola Virus Disease ◽

Equilibrium Approach ◽

Disease Free

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Challenges in Implementation of Infection Prevention and Control Measures During the Tenth Ebola Virus Disease in Northeastern of DRC, in 2019

Central African Journal of Public Health ◽

10.11648/j.cajph.20200601.13 ◽

2020 ◽

Vol 6 (1) ◽

pp. 13

Author(s):

Paul Mansiangi Mankadi ◽

Aimee Lulebo Mampasi ◽

Guillaume Kiyombo Mbela ◽

Jean-Claude Makenga Bof ◽

Jean Nyandwe ◽

...

Keyword(s):

Prevention And Control ◽

Infection Prevention ◽

Ebola Virus ◽

Virus Disease ◽

Control Measures ◽

Ebola Virus Disease ◽

Infection Prevention And Control ◽

Prevention And Control Measures ◽

And Control

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Notes from the Field: Development of a Contact Tracing System for Ebola Virus Disease — Kambia District, Sierra Leone, January–February 2015

MMWR Morbidity and Mortality Weekly Report ◽

10.15585/mmwr.mm6515a4 ◽

2016 ◽

Vol 65 (15) ◽

pp. 402 ◽

Cited By ~ 4

Author(s):

Rebecca Levine ◽

Margherita Ghiselli ◽

Agnes Conteh ◽

Bobson Turay ◽

Andrew Kemoh ◽

...

Keyword(s):

Sierra Leone ◽

Ebola Virus ◽

Virus Disease ◽

Ebola Virus Disease ◽

Contact Tracing ◽

Field Development

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ON THE GLOBAL STABILITY OF CHOLERA MODEL WITH PREVENTION AND CONTROL

MALAYSIAN JOURNAL OF COMPUTING ◽

10.24191/mjoc.v3i1.4812 ◽

2018 ◽

Vol 3 (1) ◽

pp. 28

Author(s):

M O Ibrahim ◽

A A Ayoade ◽

O J Peter ◽

F A Oguntolu

Keyword(s):

Global Stability ◽

Prevention And Control ◽

Control Measures ◽

Extended Model ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

First Order ◽

Prevention And Control Measures ◽

And Control ◽

Disease Free

In this study, a system of first order ordinary differential equations is used to analyse the dynamics of cholera disease via a mathematical model extended from Fung (2014) cholera model. The global stability analysis is conducted for the extended model by suitable Lyapunov function and LaSalle’s invariance principle. It is shown that the disease free equilibrium (DFE) for the extended model is globally asymptotically stable if 𝑅0 𝑞 < 1 and the disease eventually disappears in the population with time while there exists a unique endemic equilibrium that is globally asymptotically stable whenever 𝑅0 𝑞 > 1 for the extended model or 𝑅0 > 1 for the original model and the disease persists at a positive level though with mild waves (i.e few cases of cholera) in the case of𝑅0 𝑞 > 1. Numerical simulations for strong, weak, and no prevention and control measures are carried out to verify the analytical results and Maple 18 is used to carry out the computations.

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Ebola virus disease in pregnancy and anesthetic considerations

Journal of Hospital Administration ◽

10.5430/jha.v4n5p13 ◽

2015 ◽

Vol 4 (5) ◽

pp. 13

Author(s):

J. Sudharma Ranasinghe ◽

Andres Missair ◽

Daria Moaveni ◽

Zahira Zahid ◽

Jennifer Hochman-Cohn

Keyword(s):

Patient Population ◽

Ebola Virus ◽

Virus Disease ◽

Central Element ◽

Case Series ◽

Fetal Loss ◽

Control Measures ◽

Labor Pain ◽

Ebola Virus Disease ◽

In Pregnancy

Ebola virus disease (EVD) is often lethal, mortality rates range from 50% to over 90%, depending on the patient population, viral strain, and access to medical care. During pregnancy, the morbidity and mortality from the viral disease has been suggested to be among the highest of any affected patient population. According to the existing literature, which is confined to a few small case series in Africa, the risk of spontaneous fetal loss is high and there have been no known neonatal survivors. The mode of EVD transmission is well understood and evidence from the current and previous epidemics indicates that transmission can be interrupted by infection control measures. The central element of providing care to a patient suspected of Ebola is a three-step triage process: identify/isolate/inform. Once the diagnosis is confirmed, because of the potentially worse outcomes seen in pregnancy, specialized multidisciplinary care may be needed. In addition, especially in the obstetric setting, there is a high likelihood of exposure to a potentially deadly disease by health care workers. Therefore, these patients should be managed by anesthetic and obstetric providers in centers with expertise, protocols and training. Labor pain management, and the decision to proceed with cesarean delivery or other obstetric interventions will need to be considered on a case-by-case basis, weighing the risks and benefits to the mother, the fetus and the caregivers.

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