Modeling 2018 Ebola virus disease outbreak with Cholesky decomposition

Abstract

In this paper, we analyze a modified Susceptible‐Exposed‐Infectious‐Dead‐Recovered (SEIDR) model in the literature of the Ebola disease with uncertainties. The model is constructed using a van Kampen expansion method to have an Ebola SEIDR stochastic Fokker–Planck equation model. This model has a deterministic equation and noise covariance matrix. The basic reproduction number of the deterministic equation is calculated using the next‐generation matrix method. We prove the uniqueness and existence of the deterministic model using Lipschitz conditions and also show that it is locally asymptotically stable at it endemic equilibrium states. We constructed two equivalent stochastic differential equations (SDEs) models, whereas the Weiner process is equal to (i) the number of model equations and (ii) the number of independent changes in the model. Our aim is to solve (i) computationally using Cholesky decomposition technique with the variance–covariance matrix. Our proposed Cholesky decomposition SEIRD‐SDEs model is compared with (ii) and also with the epidemic data of the 2018 Ebola outbreak in the Democratic Republic of Congo. We also use numerical analyses to show that the importance of post‐death transmission is difficult to identify with noise terms supported by statistical hypothesis testing.