Modeling of Viral Infection with Inflammation

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

Mathematics, 2023, vol. 11, issue 19, 1-15

Abstract: Viral infection spreads in cell culture or tissue as a reaction–diffusion wave. It is characterized by three main parameters: virus replication number, R v , which determines whether infection progresses, wave speed, c , which correlates with the virus virulence, and viral load, J ( v ) , which determines the infection transmission rate. In this work, we study how the inflammation triggered by viral infection influences its progression. We obtain analytical expressions for R v , c , and J ( v ) and show how they depend on the intensity of inflammation characterized by one or two parameters. Analytical and numerical results show that inflammation decreases the viral replication number, virus virulence, and infectivity, though there are different cases depending on the parameters of the model.

Keywords: viral infection; reaction–diffusion equations; wave propagation; inflammation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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