Abstract:
The tenth Ebola outbreak in the Democratic Republic of Congo (DRC) that occurred from 2018 to 2020 was exacerbated by long-lasting conflicts and war in the region. We propose a deterministic model to investigate the impact of such disruptive events on the transmission dynamics of the Ebola virus disease. It is an extension of the classical susceptible-infectious-recovered model, enriched by an additional class of contaminated environment to account for indirect transmission as well as two classes of hospitalized individuals and patients who escape from the healthcare facility due to violence and attacks perpetrated by armed groups, rebels, etc. The model is formulated using two patches, namely Patch 1 consisting of the three affected eastern provinces in DRC and Patch 2, a war- and conflict-free area consisting of the go-to neighboring provinces for escaped patients. We introduce two key parameters, the escaping rate from hospitals and the destruction of hospitals, in terms of which the effect of war and conflicts is measured. The model is fitted and parameterized using the cumulative mortality data from the region. The basic reproduction number R0 is computed and found to have a complex expression due to the high nonlinearity of the model. By using, not a Lyapunov function, but a decomposition theorem in Castillo-Chavez et al.(in Castillo-Chavez et al. (eds) Mathematical approaches for emerging and reemerging infectious diseases: an introduction, vol 126. Springer Science & Business Media, Berlin, 2002), it is shown that the disease-free equilibrium is globally asymptotically stable when R0<1 and unstable when R0>1. A nonstandard finite difference scheme which replicates the dynamics of the continuous model is designed. In particular, a discrete counterpart of the above-mentioned theorem on the global asymptotic stability of the disease-free equilibrium is investigated. Numerical experiments are presented to support the theoretical results. When R0>1, the numerical simulations suggest that there exists for the full model a unique globally asymptotically stable interior endemic equilibrium point, while it is shown theoretically and computationally that the model possesses at least a one Patch 1 and a one Patch 2 boundary equilibria (i.e., Patch 2 and Patch 1 disease-free equilibrium) points, which are locally asymptotically stable. Some recommendations to tackle Ebola in a conflict zone are stated.
