Spatial–temporal dynamics of a novel PDE model: Applications to pharmacologic inhibition of pyroptosis by necrosulfonamide

Abstract

Most of CD4+ T cells die from pyroptosis which is an intensely inflammatory form of programmed cell death mediated by caspase-1. Inflammation is a major factor in the initiation and drive of some diseases, such as tumors, infectious diseases and atherosclerotic diseases. Recently, a new chemical inhibitor (Necrosulfonamide) has been confirmed to play a crucial role in the inhibition of pyroptosis. To provide quantitative insights into the influence of chemical inhibitor on pyroptosis, we propose a novel model of partial differential equations (PDEs) and define the basic reproduction number ℛ0. We derive the threshold-type result which is determined by the sign of ℛ0−1. Distinguished from the general viral infection dynamical models, in this model, infected cells consist of two parts: (i) the contact of uninfected cells and virus; and (ii) enhanced viral infection due to increased availability of CD4+ T cells attracted by cytokines to the inflamed sites. The formula of ℛ0 reveals that the basic reproduction number of a model that neglects the role of inflammatory cytokines IL-1β might be underevaluated. Furthermore, the basic reproduction number of a model that neglects the administration of necrosulfonamide might be overevaluated. Surprisingly, we observe that the administration of necrosulfonamide may decrease the asymptotic spreading speed of virus.