Cellular dynamical model using fractional derivatives to assess the impact of memory and host-immunity in controlling Ebola transmission

Ebola viral disease, or simply Ebola is a fatal and highly contagious disease caused by the Ebolavirus. Macrophages and dendritic immune cells are the predominant target cells of Ebolavirus. In this present study, a novel three dimensional ODE deterministic model is proposed consisting of infected target immune cells load, Ebola virions load and concentration of CTLs. The host pathogen interrelationships and role of host immunity in eliminating virions are delineated by a nonlinear functional response. The model assumes maximum concentration level of infected cells proliferation. The model is further upgraded to fractional-order system in Caputo sense and order of fractional derivatives ( ϑ ) stands for the index of immunological memory. Basic reproduction number of the system is computed as R₀ϑ = 5.1090>1 taking parameter values from real epidemiological data of Ebola in DR of Congo. The value of R₀ϑ intimates that EVD is endemic in DR of Congo and it has the potential to be more likely as pandemic. Local asymptotic stability and global asymptotic stability of the fractional-order system are analyzed around both the infection-free equilibrium and endemic equilibrium in order to determine epidemiological conditions for persistence or eventual eradication of Ebola. Sensitivity analysis of both the fractional-order model and its integer-order counterpart are carried out. Sensitivity analysis of the Caputo fractional-order system is entirely dependent on order of the fractional derivatives. The analytical findings reveal that immunological memory has substantial impact on host immune response in curtailing the chain of Ebola and they control Ebola transmission collaboratively. Extensive numerical simulations have been performed applying the generalized Adams-Bashforth-Moulton numerical scheme in support of analytical findings.