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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 non-negligible portion of individuals with an infection time, significantly longer than the mean, which may have implications on when HIV tests should be performed.
The flux of visitors through popular places undoubtedly influences viral spreading -- from H1N1 and Zika viruses spreading through physical spaces such as airports, to rumors and ideas spreading though online spaces such as chatrooms and social media
We develop a theoretical approach that uses physiochemical kinetics modelling to describe cell population dynamics upon progression of viral infection in cell culture, which results in cell apoptosis (programmed cell death) and necrosis (direct cell
Epidemic models are useful tools in the fight against infectious diseases, as they allow policy makers to test and compare various strategies to limit disease transmission while mitigating collateral damage on the economy. Epidemic models that are mo
Eigens quasi-species model describes viruses as ensembles of different mutants of a high fitness master genotype. Mutants are assumed to have lower fitness than the master type, yet they coexist with it forming the quasi-species. When the mutation ra
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species colonization and local extinction in a given g