Deterministic model for West African Ebola epidemic growth dynamics

Abstract

Previous models of Ebola epidemic growth in the affected populations of West Africa such as found in the literature have insufficient consideration of the preventive and control compartments for the models. This had led to inaccurate estimation of Ebola virus disease reproduction number and insufficient quantitative information for policy decision making of Ebola outbreak control. An improvement over those models by using additional class specifications that fully represent the Ebola epidemic dynamics is necessary. In this research, a new deterministic epidemic growth model which explains Ebola growth dynamics alongside preventive and control strategies was proposed. The Susceptible- Vaccined-Exposed-Quarantine-Infected-Hospitalised-Funeral-Recovered (SVEQIHFR) stability analysis showed that the disease-free equilibrium and the unique endemic equilibrium are asymptotically stable both locally and globally. Next generation matrix was used to determine the model threshold parameter. The threshold was found to represent the average individuals infected due to transmission from the community, hospitals and funeral events. The SVEQIHFR model was fitted to the Ebola cumulative incidence and death data of Guinea, Liberia and Sierra Leone outbreaks, collected from World Health Organization (WHO) and Center for Disease Control (CDC). Nonlinear least square method was used to estimate the model parameters and their confidence intervals were calculated using the bootstrapping method. Ebola epidemic growth threshold was estimated to be 1.28, 1.72 and 1.89 for outbreaks in Guinea, Liberia and Sierra Leone respectively. The model predicted the Ebola epidemic final size in Guinea, Liberia and Sierra Leone with 98%, 99.03% and 98.4% precision and Root Mean Square Error (RMSE) values of 0.1135, 0.1216 and 0.1167, respectively. Meanwhile the Mean Average Percentage Error (MAPE) were 22.1%, 33.2% and 20.2% for infected cases in the respective countries. Latin Hypercube Sampling (LHS) or Partial Rank Correlation Coefficient (PRCC) procedure was implemented to carry out uncertainty analysis for the model’s estimated parameters of Ebola transmission and prevalence outcome variables. It was proven that transmission coefficients and effective isolation, safe burial, effective identification and tracking of Ebola victims are critical to breaking Ebola transmission and prevalence. This model has comprehensively represented the dynamics of Ebola virus disease growth in the populations. It can help international agencies and affected countries’ public health administrators to plan for prevention and control of the spread of Ebola virus disease. The model can also be used to study similar outbreaks in the future.