Optimal control of an Ebola model with animal reservoir and environmental transmission

Abstract

A nonlinear dynamic model describes Ebola virus transmission through human infections, animal hosts, disease-induced mortality, and environmental persistence. This model consists of a human susceptible–exposed–infectious–recovered subsystem, a susceptible–infectious reservoir subsystem, and a nondimensional environmental pathogen variable governed by a Holling type-II response. Three time-dependent controls act on human-to-human transmission, animal-to-human spillover, and environmental decontamination. We establish positive invariance and boundedness and derive the controlled reproduction number, R0,c, using the next-generation matrix method. For constant controls and environmental decay, the disease-free equilibrium is locally asymptotically stable when R0,c<1, while a separate initial-condition-dependent comparison threshold gives a sufficient condition for global extinction. When R0,c>1 and the environmental couplings and human recovery rate are positive, a positive endemic equilibrium exists; global attraction is not asserted. A positivity-preserving nonstandard finite difference scheme is bounded, first-order consistent, and equilibrium preserving. Pontryagin’s maximum principle characterizes the optimal controls. Simulations with unfitted illustrative parameters describe qualitative trajectories and control mechanisms rather than predictive effect sizes. Human infection and environmental load decrease under control, whereas animal infection changes little because none of the three interventions directly controls animal-to-animal transmission or infectious-animal removal. The structural bound R0,c≥β/μa identifies this limitation of the model, not a calibrated conclusion about reservoir control.