Mathematical Analysis of the Role of Detection Rate on Dynamical Spread of Ebola Virus Disease

2020 ◽  
Vol 3 (1) ◽  
pp. 37-52
Author(s):  
Akanni John Olajide
Keyword(s):  
Detection Rate ◽  
Ebola Virus ◽  
Virus Disease ◽  
Ebola Virus Disease ◽  
Accurate Estimation ◽  
Infection Prevalence ◽  
Progression Rate ◽  
Case Detection ◽  
Case Detection Rate ◽  
Disease Free

In this paper, a non-linear mathematical model of the Ebola virus disease with case detection rate is proposed and analyzed. The whole population under consideration is divided into five compartments e.g. susceptible, latently infected, infected undetected, infected detected, and recovered to study the transmission dynamics of the Ebola virus disease. Based on the immunity level, susceptible individuals move to exposed class or directly to infected detected class once they come into contact with an infective. This has been incorporated through the progression rate which is slow. The equilibria of the model and the basic reproduction number R0 are computed. It is observed that the disease-free equilibrium of the model is locally asymptotically stable when R0<1. The model exhibits forward bifurcation under certain restrictions on parameters, which indicate that the model has a single endemic equilibrium for R0<1. This suggests that an accurate estimation of parameters and the level of control measures are required to reduce the infection prevalence of the Ebola virus in the endemic region and just R0<1 is enough to eliminate the disease from the population. R0needs to be lowered much below one to confirm the global stability of the disease-free equilibrium. Numerical simulation is performed to demonstrate the analytical results. It is found that the increase in the rate of case detection rate leads to a decrease in the threshold value of R0. Numerical simulations have been carried out to support the analytic results.

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

2018 ◽  
Vol 11 (07) ◽  
pp. 1850093 ◽  
Author(s):  
T. Berge ◽  
A. J. Ouemba Tassé ◽  
H. M. Tenkam ◽  
J. Lubuma
Keyword(s):  
Ebola Virus ◽  
Virus Disease ◽  
Control Measures ◽  
Ebola Virus Disease ◽  
Contact Tracing ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Imperfect Contact ◽  
Adequate Treatment ◽  
Disease Free

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.

scholarly journals Active Case Finding for Improved Ebola Virus Disease Case Detection in Nimba County, Liberia, 2014/2015: Lessons Learned

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
E. Namukose ◽  
C. Bowah ◽  
I. Cole ◽  
G. Dahn ◽  
P. Nyanzee ◽  
...  
Keyword(s):  
Ebola Virus ◽  
Health Workers ◽  
Virus Disease ◽  
Case Finding ◽  
Lessons Learned ◽  
Ebola Virus Disease ◽  
World Health ◽  
Case Detection ◽  
Active Case Finding ◽  
Active Case

Objectives. Early case detection and isolation of patients infected with highly infectious diseases are crucial in the management and control of epidemics such as Ebola Virus Disease (EVD). In this paper, we share the lessons learned from implementation of active case finding as a strategy for improved EVD case detection in Nimba County, Liberia. Methods. We adopted the World Health Organization (WHO) active surveillance strategy to identify and report suspected EVD cases, follow up contacts of confirmed cases, and report community deaths. We identified, trained, and deployed 1060 Community Health Volunteers (CHVs) in 718 communities in Nimba County. The CHVs were supervised by 142 health workers within their catchment area. The health workers were supervised by the District Health Officers (DHOs). The DHOs reported to the County Health Team (CHT) who provided supportive supervision. Data collection was based on the EVD contact tracing and active case finding forms adopted from WHO. Data analysis was based on epi-weeks. Results. The number of EVD suspected cases increased by more than 75% following the initiation of active case finding. Average duration between symptom onset and case detection reduced from between three and five days to within 24 hours. Collection of oral swabs from dead bodies increased from two to 15 within the first week of active case finding strategy implementation. Reporting of other IDSR priority diseases and conditions also improved. Conclusion. Active case finding strategy in Nimba increased suspected EVD case detection and reduced the duration between onset of symptoms and detection of cases.

scholarly journals Investigating the potential benefit that requiring travellers to self-isolate on arrival may have upon the reducing of case importations during international outbreaks of influenza, SARS, Ebola virus disease and COVID-19

2020 ◽  
Author(s):  
Declan Bays ◽  
Emma Bennett ◽  
Thomas Finnie
Keyword(s):  
Potential Benefit ◽  
Detection Rate ◽  
Ebola Virus ◽  
Virus Disease ◽  
International Travel ◽  
Ebola Virus Disease ◽  
Detection Rates ◽  
Potential Effectiveness

AbstractWith the advent of rapid international travel, disease can now spread between nations faster than ever. As such, when outbreaks occur in foreign states, pressure mounts to reduce the risk of importing cases to the home nation. In a previous paper, we developed a model to investigate the potential effectiveness of deploying screening at airports during outbreaks of influenza, SARS, and Ebola. We also applied the model to the current COVID-19 outbreak. This model simulated the testing of travellers (assumed not to be displaying symptoms prior to boarding their flight) as they arrived at their destination. The model showed that the reduction in risk of case importation that screening alone could deliver was minimal across most scenarios considered, with outputs indicating that screening alone could detect at most 46.4%, 12.9%, and 4.0% of travellers infected with influenza, SARS and Ebola respectively, while the model also reported a detection rate of 12.0% for COVID-19. In this paper, we present a brief modification to this model allowing us to assess the added impact that quarantining incoming travelers for various periods may have on reducing the risk of case importation. Primary results show that requiring all travellers to undergo 5 days of self-isolation on arrival, after which they are tested again, has the potential to increase rates of detection to 100%, 87.6%, 81.7% and 41.3% for travellers infected with influenza, SARS, COVID-19 and Ebola respectively. Extending the period of self-isolation to 14 days increases these potential detection rates to 100%, 100%, 99.5% and 91.8% respectively.

scholarly journals Analysis of a Multiscale Model of Ebola Virus Disease

2020 ◽  
pp. 53-69
Author(s):  
Duncan O. Oganga ◽  
George O. Lawi ◽  
Colleta A. Okaka
Keyword(s):  
Ebola Virus ◽  
Reproduction Number ◽  
Virus Disease ◽  
Equilibrium Points ◽  
Vaccination Strategy ◽  
Multiscale Model ◽  
Ebola Virus Disease ◽  
Disease Spread ◽  
The Impact ◽  
Disease Free

Multiscale models are ones that link the epidemiological processes dealing with the transmission between hosts and the immunological processes dealing with the dynamics within one host. In this study, a multiscale model of Ebola Virus Disease linking epidemiological and immunological processes has been developed and analysed. The model has considered two infectious classes ; the exposed and the infected individuals. Local and global stability analyses of the Disease Free Equilibrium and the Endemic Equilibrium points of the model show that the disease dies out if the basic reproduction number Rc0 < 1 and persists in the population when Rc0 > 1 respectively. Sensitivity analysis shows that the rate of vaccination, v , is the most sensitive parameter. This indicates that effort should be directed towards implementing an effective vaccination strategy to control the spread of the disease. It has also been established that when treatment efficacy is scaled up, the viral load goes down and consequently, the transmission between hosts is also reduced. The impact of treatment on the disease spread has also been established through the coupling function (L∗) . The study indicates that a higher percentage of the exposed and the infected individuals should be treated to control the spread of the disease within the population.

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