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.
Keywords: Continuous-time and space branching Markov processes, Structured population, Long time behaviour, Birth and Death Processes
@article{MSIA_2023__12_1_23_0, author = {Charline Smadi}, title = {Parasite infection in a cell population with deaths and reinfections}, journal = {MathematicS In Action}, pages = {23--47}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {12}, number = {1}, year = {2023}, doi = {10.5802/msia.30}, language = {en}, url = {https://msia.centre-mersenne.org/articles/10.5802/msia.30/} }
TY - JOUR AU - Charline Smadi TI - Parasite infection in a cell population with deaths and reinfections JO - MathematicS In Action PY - 2023 SP - 23 EP - 47 VL - 12 IS - 1 PB - Société de Mathématiques Appliquées et Industrielles UR - https://msia.centre-mersenne.org/articles/10.5802/msia.30/ DO - 10.5802/msia.30 LA - en ID - MSIA_2023__12_1_23_0 ER -
%0 Journal Article %A Charline Smadi %T Parasite infection in a cell population with deaths and reinfections %J MathematicS In Action %D 2023 %P 23-47 %V 12 %N 1 %I Société de Mathématiques Appliquées et Industrielles %U https://msia.centre-mersenne.org/articles/10.5802/msia.30/ %R 10.5802/msia.30 %G en %F MSIA_2023__12_1_23_0
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] 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] 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] Phage-displayed mimotopes elicit monoclonal antibodies specific for a malaria vaccine candidate, Biol. Chem., Volume 379 (1998), pp. 65-70
[4] 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] 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] 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] On the extinction of continuous state branching processes with catastrophes, Electron. J. Probab., Volume 18 (2013), pp. 1-31 | DOI | MR | Zbl
[8] On the scaling limits of Galton-Watson processes in varying environments, Electron. J. Probab., Volume 20 (2015) | MR | Zbl
[9] 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] Phage biology, Phages: their role in bacterial pathogenesis and biotechnology, Wiley Publishing, 2005, pp. 18-36
[11] Limit theorems for some branching measure-valued processes, Adv. Appl. Probab., Volume 49 (2017) no. 2, pp. 549-580 | DOI | MR | Zbl
[12] Oxford textbook of global public health, 2, Oxford Textbook, 2015 | DOI
[13] Branching process models of cancer, Branching process models of cancer, Springer, 2015, pp. 1-63 | Zbl
[14] 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] A spine approach to branching diffusions with applications to -convergence of martingales, Séminaire de probabilités XLII, Springer, 2009, pp. 281-330 | DOI | Zbl
[16] Stochastic differential equations and diffusion processes, 24, Elsevier, 1989
[17] 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] Evolving phage vectors for cell targeted gene delivery, Curr. Pharm. Biotechnol., Volume 3 (2002) no. 1, pp. 45-57 | DOI
[19] A general continuous-state nonlinear branching process, Ann. Appl. Probab., Volume 29 (2019) no. 4, pp. 2523-2555 | MR | Zbl
[20] Uniform sampling in a structured branching population, Bernoulli, Volume 25 (2016), pp. 2649-2695 | DOI | MR | Zbl
[21] Long time behaviour of continuous-state nonlinear branching processes with catastrophes, Electron. J. Probab., Volume 26 (2021), pp. 1-32 | MR | Zbl
[22] Spread of parasites affecting death and division rates in a cell population (2022) (https://arxiv.org/abs/2211.08265)
[23] Parasite infection in a cell population: role of the partitioning kernel (2023) (https://arxiv.org/abs/2305.06962)
[24] Evolutive two-level population process and large population approximations, Ann. Univ. Buchar., Math. Ser., Volume 4 (2013), pp. 37-70 | MR | Zbl
[25] 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] Two level branching model for virus population under cell division (2020) (https://arxiv.org/abs/2004.14352)
[27] Branching processes in a Lévy random environment, Acta Appl. Math., Volume 153 (2018) no. 1, pp. 55-79 | DOI | Zbl
[28] Stochastic differential equations, Stochastic integration and differential equations, Springer, 2005, pp. 249-361 | DOI
[29] Introduction to phage biology and phage display, Phage Display: A practical approach, Oxford University Press, 2004, pp. 1-26
[30] Some physical-chemical and biological properties of the rod-shaped coliphage M13, Virology, Volume 24 (1964) no. 3, pp. 359-371 | DOI
[31] Stochastic dynamics of an epidemic with recurrent spillovers from an endemic reservoir, J. Theor. Biol., Volume 457 (2018), pp. 37-50 | DOI | MR | Zbl
Cited by Sources: