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

Joseph E. Carroll; Joseph E. Carroll

doi:10.3934/mbe.2022522

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 11195-11216. doi: 10.3934/mbe.2022522

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

Joseph E. Carroll ^{1,2,3
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1.
Department of Mathematics, California State Polytechnic University, Humboldt
2.
Department of Family Medicine, Oregon Health and Science University
3.
Providence/St. Joseph Eureka Family Medicine Residency

Academic Editor: Frithjof Lutscher

Received: 29 April 2022 Revised: 16 July 2022 Accepted: 24 July 2022 Published: 04 August 2022

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.
- delay-differential equations,
- viral infection dynamics,
- transcendental polynomial
Citation: Joseph E. Carroll. A two-dimensional discrete delay-differential system model of viremia[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11195-11216. doi: 10.3934/mbe.2022522

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Abstract

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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