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Dynamics of epidemic models with asymptomatic infection and seasonal succession
See publicationIn this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which means the system is periodic and discontinuous. We defined its basic reproduction number (BRN), an important threshold parameter that decides if the disease will spread. We found that when RBN is less than or equal to one, the disease will die out in the end, otherwise it will prevail.
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Modeling calcium waves in an anatomically accurate three-dimensional parotid acinar cell
Journal of Theoretical Biology
See publicationWe construct a model of calcium waves in a three-dimensional anatomically accurate parotid acinar cell, constructed from experimental data. Gradients of inositol trisphosphate receptor (IPR) density are imposed, with the IPR density being greater closer to the lumen, which has a branched structure, and inositol trisphosphate (IP3) is produced only at the basal membrane.
We show (1) that IP3 equilibrates so quickly across the cell that it can be assumed to be spatially homogeneous; (2)…We construct a model of calcium waves in a three-dimensional anatomically accurate parotid acinar cell, constructed from experimental data. Gradients of inositol trisphosphate receptor (IPR) density are imposed, with the IPR density being greater closer to the lumen, which has a branched structure, and inositol trisphosphate (IP3) is produced only at the basal membrane.
We show (1) that IP3 equilibrates so quickly across the cell that it can be assumed to be spatially homogeneous; (2) spatial separation of the sites of IP3 action and IP3 production does not preclude the formation of stable oscillatory Ca2+ waves. However, these waves are not waves in the mathematical sense of a traveling wave with fixed profile. They result instead from a time delay between the Ca2+ rise in the apical and basal regions; (3) the ryanodine receptors serve to reinforce the Ca2+ wave, but are not necessary for the wave to exist; (4) a spatially independent model is not sufficient to study saliva secretion, although a one-dimensional model might be sufficient. Our results here form the first stages of the construction of a multiscale and multicellular model of saliva secretion in an entire acinus.
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