Parasite infection in a cell population with deaths and reinfections
MathematicS In Action, Maths Bio, Volume 12 (2023) no. 1, pp. 23-47.

We introduce a model of parasite infection in a cell population, where cells can be infected, either at birth through maternal transmission, from a contact with the parasites reservoir, or because of the parasites released in the cell medium by infected cells. Inside the cells and between infection events, the quantity of parasites evolves as a general non linear branching process. We study the long time behaviour of the infection.

Published online:
DOI: 10.5802/msia.30
Classification: 60J80, 60J85, 60H10
Keywords: Continuous-time and space branching Markov processes, Structured population, Long time behaviour, Birth and Death Processes
Charline Smadi 1, 2

1 Univ. Grenoble Alpes, INRAE, LESSEM, 38000 Grenoble, France
2 Univ. Grenoble Alpes, CNRS, Institut Fourier, 38000 Grenoble, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Charline Smadi. Parasite infection in a cell population with deaths and reinfections. MathematicS In Action, Maths Bio, Volume 12 (2023) no. 1, pp. 23-47. doi : 10.5802/msia.30. https://msia.centre-mersenne.org/articles/10.5802/msia.30/

[1] Gerold Alsmeyer; Sören Gröttrup A host-parasite model for a two-type cell population, Adv. Appl. Probab., Volume 45 (2013) no. 3, pp. 719-741 | DOI | MR | Zbl

[2] Gerold Alsmeyer; Sören Gröttrup Branching within branching: A model for host–parasite co-evolution, Stochastic Processes Appl., Volume 126 (2016) no. 6, pp. 1839-1883 | DOI | MR | Zbl

[3] Farida Nato Alzari; Shirley Longacre; Pierre Lafaye; Jean-Claude Mazie Phage-displayed mimotopes elicit monoclonal antibodies specific for a malaria vaccine candidate, Biol. Chem., Volume 379 (1998), pp. 65-70

[4] Vincent Bansaye Proliferating parasites in dividing cells: Kimmel’s branching model revisited, Ann. Appl. Probab., Volume 18 (2008) no. 3, pp. 967-996 | DOI | MR | Zbl

[5] Vincent Bansaye Cell contamination and branching processes in a random environment with immigration, Adv. Appl. Probab., Volume 41 (2009) no. 4, pp. 1059-1081 | DOI | MR | Zbl

[6] Vincent Bansaye; Jean-François Delmas; Laurence Marsalle; Viet Chi Tran Limit theorems for Markov processes indexed by continuous time Galton–Watson trees, Ann. Appl. Probab., Volume 21 (2011) no. 6, pp. 2263-2314 | MR | Zbl

[7] Vincent Bansaye; Juan Carlos Pardo; Charline Smadi On the extinction of continuous state branching processes with catastrophes, Electron. J. Probab., Volume 18 (2013), pp. 1-31 | DOI | MR | Zbl

[8] Vincent Bansaye; Florian Simatos On the scaling limits of Galton-Watson processes in varying environments, Electron. J. Probab., Volume 20 (2015) | MR | Zbl

[9] Vincent Bansaye; Viet Chi Tran Branching Feller diffusion for cell division with parasite infection, ALEA, Lat. Am. J. Probab. Math. Stat., Volume 8 (2011), pp. 95-127 | MR | Zbl

[10] Richard Calendar; Ross Inman Phage biology, Phages: their role in bacterial pathogenesis and biotechnology, Wiley Publishing, 2005, pp. 18-36

[11] Bertrand Cloez Limit theorems for some branching measure-valued processes, Adv. Appl. Probab., Volume 49 (2017) no. 2, pp. 549-580 | DOI | MR | Zbl

[12] Roger Detels Oxford textbook of global public health, 2, Oxford Textbook, 2015 | DOI

[13] Richard Durrett Branching process models of cancer, Branching process models of cancer, Springer, 2015, pp. 1-63 | Zbl

[14] Hans-Otto Georgii; Ellen Baake Supercritical multitype branching processes: the ancestral types of typical individuals, Adv. Appl. Probab., Volume 35 (2003) no. 4, pp. 1090-1110 | DOI | MR | Zbl

[15] Robert Hardy; Simon C. Harris A spine approach to branching diffusions with applications to L p -convergence of martingales, Séminaire de probabilités XLII, Springer, 2009, pp. 281-330 | DOI | Zbl

[16] Nobuyuki Ikeda; Shinzo Watanabe Stochastic differential equations and diffusion processes, 24, Elsevier, 1989

[17] Marek Kimmel Quasistationarity in a branching model of division-within-division, Classical and modern branching processes (Minneapolis, MN, 1994) (The IMA Volumes in Mathematics and its Applications), Volume 84, Springer, 1997, pp. 157-164 | DOI | MR | Zbl

[18] David Larocca; M. A. Brug; Kristen Jensen-Pergakes; E. Ravey; Ana Gonzalez; Andrew Baird Evolving phage vectors for cell targeted gene delivery, Curr. Pharm. Biotechnol., Volume 3 (2002) no. 1, pp. 45-57 | DOI

[19] Pei-Sen Li; Xu Yang; Xiaowen Zhou A general continuous-state nonlinear branching process, Ann. Appl. Probab., Volume 29 (2019) no. 4, pp. 2523-2555 | MR | Zbl

[20] Aline Marguet Uniform sampling in a structured branching population, Bernoulli, Volume 25 (2016), pp. 2649-2695 | DOI | MR | Zbl

[21] Aline Marguet; Charline Smadi Long time behaviour of continuous-state nonlinear branching processes with catastrophes, Electron. J. Probab., Volume 26 (2021), pp. 1-32 | MR | Zbl

[22] Aline Marguet; Charline Smadi Spread of parasites affecting death and division rates in a cell population (2022) (https://arxiv.org/abs/2211.08265)

[23] Aline Marguet; Charline Smadi Parasite infection in a cell population: role of the partitioning kernel (2023) (https://arxiv.org/abs/2305.06962)

[24] Sylvie Méléard; Sylvie Rœlly Evolutive two-level population process and large population approximations, Ann. Univ. Buchar., Math. Ser., Volume 4 (2013), pp. 37-70 | MR | Zbl

[25] Annalisa Meola; Paola Delmastro; Paolo Monaci; Alessandra Luzzago; Alfredo Nicosia; Franco Felici; Riccardo Cortese; Giovanni Galfrè Derivation of vaccines from mimotopes. Immunologic properties of human hepatitis B virus surface antigen mimotopes displayed on filamentous phage., J. Immunol., Volume 154 (1995) no. 7, pp. 3162-3172 | DOI

[26] Luis Osorio; Anita Winter Two level branching model for virus population under cell division (2020) (https://arxiv.org/abs/2004.14352)

[27] Sandra Palau; Juan Carlos Pardo Branching processes in a Lévy random environment, Acta Appl. Math., Volume 153 (2018) no. 1, pp. 55-79 | DOI | Zbl

[28] Philip E. Protter Stochastic differential equations, Stochastic integration and differential equations, Springer, 2005, pp. 249-361 | DOI

[29] Marjorie Russel; Henry B. Lowman; Tim Clackson Introduction to phage biology and phage display, Phage Display: A practical approach, Oxford University Press, 2004, pp. 1-26

[30] William O. Salivar; Helen Tzagoloff; David Pratt Some physical-chemical and biological properties of the rod-shaped coliphage M13, Virology, Volume 24 (1964) no. 3, pp. 359-371 | DOI

[31] Marina Voinson; Alexandra Alvergne; Sylvain Billiard; Charline Smadi Stochastic dynamics of an epidemic with recurrent spillovers from an endemic reservoir, J. Theor. Biol., Volume 457 (2018), pp. 37-50 | DOI | MR | Zbl

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