We study the early stages of viral infection, and the distribution of times to obtain a persistent infection. The virus population proliferates by entering and reproducing inside a target cell until a sufficient number of new virus particles are released via a burst, with a given burst size distribution, which results in the death of the infected cell. Starting with a 2D model describing the joint dynamics of the virus and infected cell populations, we analyze the corresponding master equation using the probability generating function formalism. Exploiting time-scale separation between the virus and infected cell dynamics, the 2D model can be cast into an effective 1D model. To this end, we solve the 1D model analytically for a particular choice of burst size distribution. In the general case, we solve the model numerically by performing extensive Monte-Carlo simulations, and demonstrate the equivalence between the 2D and 1D models by measuring the Kullback-Leibler divergence between the corresponding distributions. Importantly, we find that the distribution of infection times is highly skewed with a 'fat' exponential right tail. This indicates that there is a non-negligible portion of individuals with an infection time, significantly longer than the mean, which may have implications on, e.g., when HIV tests should be performed.
|Original language||American English|
|Journal||Journal of Statistical Mechanics: Theory and Experiment|
|State||Published - 25 Jun 2019|
Bibliographical notePublisher Copyright:
© 2019 IOP Publishing Ltd and SISSA Medialab srl.
- classical monte carlo simulations
- fluctuation phenomena
- population dynamics
- stochastic processes