Mathematical Modelling of the Transmission Dynamics of Ebola Virus

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.

Download Full-text

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.

Download Full-text

Transmission dynamics of Ebola virus disease and intervention effectiveness in Sierra Leone

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1518587113 ◽

2016 ◽

Vol 113 (16) ◽

pp. 4488-4493 ◽

Cited By ~ 52

Author(s):

Li-Qun Fang ◽

Yang Yang ◽

Jia-Fu Jiang ◽

Hong-Wu Yao ◽

David Kargbo ◽

...

Keyword(s):

Sierra Leone ◽

Ebola Virus ◽

Virus Disease ◽

Atmospheric Temperature ◽

Transmission Dynamics ◽

Ebola Virus Disease ◽

Transmission Model ◽

Household Transmission ◽

Secondary Infections ◽

The Impact

Sierra Leone is the most severely affected country by an unprecedented outbreak of Ebola virus disease (EVD) in West Africa. Although successfully contained, the transmission dynamics of EVD and the impact of interventions in the country remain unclear. We established a database of confirmed and suspected EVD cases from May 2014 to September 2015 in Sierra Leone and mapped the spatiotemporal distribution of cases at the chiefdom level. A Poisson transmission model revealed that the transmissibility at the chiefdom level, estimated as the average number of secondary infections caused by a patient per week, was reduced by 43% [95% confidence interval (CI): 30%, 52%] after October 2014, when the strategic plan of the United Nations Mission for Emergency Ebola Response was initiated, and by 65% (95% CI: 57%, 71%) after the end of December 2014, when 100% case isolation and safe burials were essentially achieved, both compared with before October 2014. Population density, proximity to Ebola treatment centers, cropland coverage, and atmospheric temperature were associated with EVD transmission. The household secondary attack rate (SAR) was estimated to be 0.059 (95% CI: 0.050, 0.070) for the overall outbreak. The household SAR was reduced by 82%, from 0.093 to 0.017, after the nationwide campaign to achieve 100% case isolation and safe burials had been conducted. This study provides a complete overview of the transmission dynamics of the 2014−2015 EVD outbreak in Sierra Leone at both chiefdom and household levels. The interventions implemented in Sierra Leone seem effective in containing the epidemic, particularly in interrupting household transmission.

Download Full-text