Assessing the impact of the environmental contamination on the transmission of Ebola virus disease (EVD)

This paper deals with the following biological question: how influential is the environmental contamination on the transmission of EVD? Based on the works in (Bibby et al., Environ Sci Technol Lett 2:2–6, 2015; Leroy et al., Nature 438: 575–576, 2005; World Health Organization. Unprecedented number of medical staff infected with Ebola), we design a new mathematical model to address this question by assessing the effect of the Ebola virus contaminated environment on the dynamical transmission of EVD. The formulated model captures two infection pathways through both direct human-to-human transmission and indirect human-to-environment-to-human transmission by incorporating the environment as a transition and/or reservoir of Ebola viruses. We compute the basic reproduction number \({\mathcal {R}}^{env}_0\) for the model with environmental contamination and prove that the disease-free equilibrium is globally asymptotically stable (GAS) whenever \({\mathcal {R}}^{env}_0 \le 1\). When \({\mathcal {R}}^{env}_0 > 1\), we show that the said model has a unique endemic equilibrium which is GAS. Similar results hold for the free environmental contamination sub-model (without the incorporation of the indirect transmission). More precisely, for the latter model, calculate the corresponding basic reproduction number \({\mathcal {R}}^{h}_0\) and establish the GAS of the disease-free and endemic equilibria, whenever \({\mathcal {R}}^{h}_0 \le 1\) and \({\mathcal {R}}^{h}_0 > 1\), respectively. At the endemic level, we show that the number of infected individuals for the full model with the environmental contamination is greater than the corresponding number for the free environmental contamination sub-model. In conjunction with the inequality \({\mathcal {R}}^{h}_0 < {\mathcal {R}}^{env}_0\), our finding suggests a negative answer to the biological question under investigation, i.e. the contaminated environment plays a detrimental role on the transmission dynamics of EVD by increasing the endemic level and/or the severity of the outbreak. Therefore, it is natural to implement a control strategy which aim at reducing the severity of the disease by providing adequate hygienic living conditions, educate populations at risk to follow rigorously those basic hygienic conditions as well as ask them avoid contact with suspected contaminated objects. Further, we perform numerical simulations to support the theory.