A two-dimensional discrete delay-differential system model of viremia

A deterministic model is proposed to describe the interaction between an immune system and an invading virus whose target cells circulate in the blood. The model is a system of two ordinary first order quadratic delay-differential equations with stipulated initial conditions, whose coefficients are...

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Published inMathematical biosciences and engineering : MBE Vol. 19; no. 11; pp. 11195 - 11216
Main Author Carroll, Joseph E.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
delay-differential equations
transcendental polynomial
viral infection dynamics
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Summary:A deterministic model is proposed to describe the interaction between an immune system and an invading virus whose target cells circulate in the blood. The model is a system of two ordinary first order quadratic delay-differential equations with stipulated initial conditions, whose coefficients are eventually constant, so that the system becomes autonomous. The long-term behavior of the solution is investigated with some success. In particular, we find two simple functions of the parameters of the model, whose signs often, but not always, determine whether the virus persists above a nonzero threshold in the circulation or heads toward extinction.
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ISSN:1551-0018
1551-0018
DOI:10.3934/mbe.2022522