Global Dynamics of Viral Infection with Two Distinct Populations of Antibodies

Ahmed M. Elaiw (), Aeshah A. Raezah and Matuka A. Alshaikh
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Ahmed M. Elaiw: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Aeshah A. Raezah: Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia
Matuka A. Alshaikh: Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Mathematics, 2023, vol. 11, issue 14, 1-26

Abstract: This paper presents two viral infection models that describe dynamics of the virus under the effect of two distinct types of antibodies. The first model considers the population of five compartments, target cells, infected cells, free virus particles, antibodies type-1 and antibodies type-2. The presence of two types of antibodies can be a result of secondary viral infection. In the second model, we incorporate the latently infected cells. We assume that the antibody responsiveness is given by a combination of the self-regulating antibody response and the predator–prey-like antibody response. For both models, we verify the nonnegativity and boundedness of their solutions, then we outline all possible equilibria and prove the global stability by constructing proper Lyapunov functions. The stability of the uninfected equilibrium EQ 0 and infected equilibrium EQ * is determined by the basic reproduction number R 0 . The theoretical findings are verified through numerical simulations. According to the outcomes, the trajectories of the solutions approach EQ 0 and EQ * when R 0 ≤ 1 and R 0 > 1 , respectively. We study the sensitivity analysis to show how the values of all the parameters of the suggested model affect R 0 under the given data. The impact of including the self-regulating antibody response and latently infected cells in the viral infection model is discussed. We showed that the presence of the self-regulating antibody response reduces R 0 and makes the system more stabilizable around EQ 0 . Moreover, we established that neglecting the latently infected cells in the viral infection modeling leads to the design of an overflow of antiviral drug therapy.

Keywords: viral infection; antibody immune response; global stability; Lyapunov function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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