Mathematical Model of Infection Propagation Mediated by Circulating Macrophages

Meriem Bouzari, Latifa Ait Mahiout (), Anastasia Mozokhina and Vitaly Volpert ()
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Meriem Bouzari: Laboratoire D’équations aux Dérivées Partielles non Linéaires et Histoire des Mathématiques, École Normale Supérieure, B.P. 92, Vieux Kouba, Algiers 16050, Algeria
Latifa Ait Mahiout: Laboratoire D’équations aux Dérivées Partielles non Linéaires et Histoire des Mathématiques, École Normale Supérieure, B.P. 92, Vieux Kouba, Algiers 16050, Algeria
Anastasia Mozokhina: S.M. Nikol’skii Mathematical Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia
Vitaly Volpert: S.M. Nikol’skii Mathematical Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia

Mathematics, 2025, vol. 13, issue 21, 1-17

Abstract: We develop and analyze a reaction-diffusion model describing the early spatial dynamics of viral infection in tissue, incorporating key components of the innate immune system: inflammatory cytokines and circulating macrophages. The system couples three spatial partial differential equations (for uninfected cells, infected cells, and virus particles) with two ordinary differential equations (for cytokines and activated macrophages), and it includes time delays related to intracellular viral replication. In the absence of macrophage degradation, we derive analytical expressions for the total viral load and the wave speed, and we identify explicit immune control thresholds in terms of the virus replication number and the strength of the immune response. In the presence of macrophage degradation, simulations reveal that increasing macrophage turnover accelerates wave propagation and increases viral burden. These results highlight the critical role of innate immune feedback, modulated by effector degradation, in shaping the spatial outcome of infection. Depending on the values of viral replication number and the strength of the immune response, infection can be immediately suppressed, or it can propagate with gradual extinction due to the time-dependent immune response, or it can persistently propagate in the tissue in the form of a reaction-diffusion wave.

Keywords: infection propagation; innate immunity; cytokine signaling; macrophage activation; reaction-diffusion system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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