ABSTRACT
Chapter 4 deals with five models of epidemic spread and outbreak dynamics of Ebola virus. Model 1 is an Ebola epidemic SEIR-type model. The nonspatial model is analyzed for the equilibrium points, the calculation of the basic reproduction number 1, the stability of equilibrium points, bifurcation, and sensitivity analysis. The one- and two-dimensional spatial SEIR models are analyzed for Turing instability and spatiotemporal pattern formations. Model 2 is an Ebola epidemic SEIRHD model that is a modification of the first model by considering three different transmission routes, 2, 3, and 4. The spatial version of the model is also discussed, and the numerical simulation results are presented for spatiotemporal patterns in two dimensions. Model 3 is an Ebola epidemic SEIORD model and its extension by including the potential impact of limited hospital beds on EVD dynamics. The equilibrium points are analyzed for its stability, and the optimal control problem is discussed. Model 4 is an Ebola epidemic SEIRD time delay model. Existence of the equilibrium point is studied, and the basic reproduction number is calculated using the next infection operator. Model 5 is a general Ebola transmission model designed by Agusto et al. for the transmission dynamics of EVD in a population stratified into two epidemiological settings: (i) in the community and (ii) within the healthcare system. Bifurcation analysis is done analytically and numerically. Time series analysis is presented to study the effect of reinfection and relapse on early infected class.
