Stability Analysis of a Delayed Immune Response Model to Viral Infection

Abstract

The purpose of this work is the study of the qualitative behavior of the homogeneous in space solution of a delay differential equation arising from a model of infection dynamics. This study is mainly based on the monotone dynamical systems theory. Existence and smoothness of solutions are proved, and conditions of asymptotic stability of equilibriums in the sense of monotone dynamical systems are formulated. Then, sufficient conditions of global stability of the nonzero steady state are derived, for the two typical forms of the function f, specifying the efficiency of immune response-mediated virus elimination. Numerical simulations illustrate the analytical results. The obtained theoretical results have been applied, in a context of COVID-19 data calibration, to forecast the immunological behaviour of a real patient.

Stability Analysis of a Viral Immune Response Model Involving Two Time Delays

“…In the present paper, we genralize the work presented in [6] where authors considered the same model but with a single time delay and they establish sufficient conditions of asymptotic and global stability for the equilibria. We shall prove that under suitable conditions on model's parameters the equilibrium are asymptotically stable.…”

“…Let h be defined by (6). Suppose that h is continuously differentiable in a neighbourhood of an equilibirum x * of (7) and dh(x * ) verifies (L µ ) for some µ > 0, then…”

System Complexity in Influenza Infection and Vaccination: Effects upon Excess Winter Mortality

“…Regarding the multiple equilibria, the immune system does indeed exist in multiple steady states [ 37 , 38 , 39 , 40 , 41 , 42 ]. Such immune-endocrine steady states can correspond to certain illnesses, such as Gulf War illness and chronic fatigue syndrome [ 38 ].…”