Queueing theory based model and network analysis for predicting the transmission and control of ebola virus disease

Abstract

Ebola Virus Disease (EVD) is a complex epidemic killer disease. Recently, the disease has caused serious loss of life, waste of economy and material resources in West Africa nations. Literature shows that mathematical theories and models such as agent-based model, models based on ordinary differential equation for assessment studies and intervention measures have been proposed by several researchers to handle the outbreak of the disease. But, agent-based model comes with high computational cost, and model based on ordinary differential equation describes reality with varying accuracy. Therefore, there is the need for a mathematical model that can describe the real nature of the disease, reduce computational cost and better prediction of its behaviour. This study presents the modelling and analysis of EVD transmission and control using queueing theory technique. Data collected from WHO Ebola Data and Statistics of the recent outbreak in Guinea, Liberia and Sierra Leone from December 2013 to July 2015 is used in the study. The SEILICDR (Susceptible, Exposed, Likely Infected, Confirmed Infected, Dead/Recovery) Ebola epidemic model is proposed to accommodate all the transmission phases and be able to explain EVD transmission and control reliably. The EVD transmission patterns and possible control measures are determined using the basic properties of queueing theory. The SEILICDR based compartmental model is obtained, where SEILICDR represent the compartments within the countries. In addition, the SEILICDR based network model is also developed to characterize every interpersonal contact that can potentially lead to disease transmission. Findings indicate that the spread of EVD follows an irregular and random pattern. Also, the SEILICDR model shows that the Quasi-Stationary Distribution approximation is better than the existing models for the description of EVD problems. Result of the application of queueing theory yielded that the developed model is a reasonable approximation, showing when Ebola Virus is controlled. While, result from network model indicates that the population is vulnerable to large scale epidemics before intervention in the three countries. The vulnerability decreased drastically after intervention. The researcher recommends that studies need to be conducted to include other continent of the world affected by Ebola Virus Disease. The underlying factors of the epidemic are changing rapidly with the increase in safety measures, researchers should develop model that can predict cases in such situation.