Homogenization of a reaction diffusion equation can explain influenza A virus load data

JOURNAL OF THEORETICAL BIOLOGY

卷:527

Article

Baabdulla, Arwa Abdulla¹  Now, Hesung²  Park, Ju An³  Kim, Woo-Jong²  Jung, Sungjune^3,4  Yoo, Joo-Yeon²  Hillen, Thomas¹ 

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB, Canada

[2] Pohang Univ Sci & Technol, Dept Life Sci, Pohang, South Korea

[3] Pohang Univ Sci & Technol, Dept Mat Sci & Engn, Pohang, South Korea

[4] Pohang Univ Sci & Technol, Sch Interdisciplinary Biosci & Bioengn, Pohang, South Korea

关键词: Virus load;    Spatial viral distribution;    Homogenization method;    Fisher-KPP equation;    Arithmetic mean;    Harmonic mean;   

DOI  :  10.1016/j.jtbi.2021.110816

来源: Elsevier

【 摘 要 】

We study the influence of spatial heterogeneity on the antiviral activity of mouse embryonic fibroblasts (MEF) infected with influenza A. MEF of type Ube1L(-/-) are composed of two distinct sub-populations, the strong type that sustains a strong viral infection and the weak type, sustaining a weak viral load. We present new data on the virus load infection of Ube1L(-/-), which have been micro-printed in a checker board pattern of different sizes of the inner squares. Surprisingly, the total viral load at one day after inoculation significantly depends on the sizes of the inner squares. We explain this observation by using a reaction diffusion model and we show that mathematical homogenization can explain the observed inhomogeneities. If the individual patches are large, then the growth rate and the carrying capacity will be the arithmetic means of the patches. For finer and finer patches the average growth rate is still the arithmetic mean, however, the carrying capacity uses the harmonic mean. While fitting the PDE to the experimental data, we also predict that a discrepancy in virus load would be unobservable after only half a day. Furthermore, we predict the viral load in different inner squares that had not been measured in our experiment and the travelling distance the virions can reach after one day. (C) 2021 Elsevier Ltd. All rights reserved.

【 授权许可】

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