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HW Thompson, D Bloom, HE Kaufman, JM Hill; A Mathematical Model of HSV-1 Infection, Latency, and Reactivation in the Corneal Epithelium and Trigeminal Ganglion . Invest. Ophthalmol. Vis. Sci. 2002;43(13):4316.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose: To devise a mathematical model of the dynamics of viral proliferation, clearance, and latency in the cornea (CO) - trigeminal ganglion (TG) pathway that would be useful in prediction of latency, reactivation, and drug action (inhibition). Methods: Using values for virus copy numbers, clearance rates, axonal transport rates, and number of latent virus genomic copy numbers obtained from published experimental data, a differential equation model of the system was devised. Numerical results were produced by computation based on the solution of the equation system. Results: A model was devised in which the CO and TG are compartments connected by axonal transport from the trigeminal ganglion to the cornea (TG ≷ CO) and from the cornea to the trigeminal ganglion (CO ≷ TG). The model consists of the coupled simultaneous differential equations: dVco/dt = pVco - (c+L)Vco + rVtg ; dVtg/dt = LVo + pVtg - rVtg, where dVco/dt and dVtg/dt are the rates of virus production over time in the CO and TG respectively; pVco and pVtg are production rates of virus in the CO and TG; LVco is the flow rate of virus from the cornea to the trigeminal ganglion (CO ≷ TG); rVtg is the flow rate of virus from the trigeminal ganglion to the cornea (TG ≷ CO); and cVco is the clearance rate of virus from CO. At zero CO virus production, no input from TG (r=0), and no loss to TG (L=0), the concentration of infectious virus will fall exponentially due to clearance from CO; this rate of fall would be augmented if transport to TG were not 0 (r!=0). If viral concentration in CO begins at a low level and there is a loss due to latency (CO ≷ TG) as well as a positive influx from the TG (r!=0), clearance can be overcome by low influx and, after a time lag, the number of virus particles will increase at an exponential rate (acute recurrence). Conclusion: The model uses experimental data as input to predict the outcome following an initial viral inoculum of a specified concentration. The model predicts different proliferation rates under various conditions, e.g., if drug treatment reduces viral load or proliferation rates, or if fewer virions are transported. Using this model, predictions for a wide variety of conditions of the CO-TG system have been developed and will be presented.
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