On the global attractors in one mathematical model of antiviral immunity

Alexei Tsygvintsev

doi:10.5802/crmath.140

Systèmes dynamiques

On the global attractors in one mathematical model of antiviral immunity
[Sur les attracteurs globaux dans un modèle mathématique de l’immunité antivirale]

Alexei Tsygvintsev ¹

¹ ENS de Lyon, UMPA, 46 allée d’Italie, 69364 Lyon Cedex 07, FRANCE

Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1199-1205.

Abstract (VO)
Résumé

We consider the mathematical model introduced by Batholdy et al. [1] describing the interaction between viral pathogens and immune system. We prove the global asymptotic stability of the infection steady-state if the basic reproductive ratio $R_{0}$ is greater than unity. That solves the conjecture announced in [7].

Nous considérons le modèle mathématique introduit par Batholdy et al. [1] décrivant l’interaction entre les agents pathogènes viraux et le système immunitaire. Nous prouvons la stabilité globale asymptotique de l’état d’équilibre de l’infection si le taux de reproduction de base $R_{0}$ est supérieur à $1$ . Cela résout la conjecture annoncée dans [7].

Reçu le : 2020-10-16
Révisé le : 2020-10-21
Accepté le : 2020-10-27
Publié le : 2021-01-25

DOI : 10.5802/crmath.140

Classification : 92B05

Affiliations des auteurs :

Alexei Tsygvintsev ¹

¹ ENS de Lyon, UMPA, 46 allée d’Italie, 69364 Lyon Cedex 07, FRANCE

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Alexei Tsygvintsev},
     title = {On the global attractors in one mathematical model of antiviral immunity},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1199--1205},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {11-12},
     year = {2020},
     doi = {10.5802/crmath.140},
     language = {en},
}

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Alexei Tsygvintsev. On the global attractors in one mathematical model of antiviral immunity. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1199-1205. doi : 10.5802/crmath.140. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.140/

Bibliographie
Cité par

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[8] Robert F. Williams The structure of Lorenz attractors, Publ. Math., Inst. Hautes Étud. Sci., Volume 50 (1979), pp. 73-99 | DOI | Numdam | Zbl

[9] Dominik Wodarz; Jan Pravsgaard Christensen; Allan Randrup Thomsen The importance of lytic and non-lytic immune responses in viral infections, Trends Immunol., Volume 23 (2002) no. 4, pp. 194-200 | DOI

[10] Carolin Zitzmann; Lars Kaderali Mathematical Analysis of Viral Replication Dynamics and Antiviral Treatment Strategies: From Basic Models to Age-Based Multi-Scale Modeling, Front. Microbiol., Volume 9 (2018), 1546 | DOI

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