Virus Dispersal in Bacterial Colonies

Here V, B, and I denote virus, host bacteria, and infected bacteria, respectively. Y is the production or yield of new viruses per host. We focus on the relevant factors by excluding negligible reactions, such as virus desorption and their adsorption to infected hosts. Consider a homogeneous medium composed initially of host bacteria and a few free viruses. The adsorption process can be described by the classical kinetic equations 

The replication process begins when the virus injects its DNA into the bacterium. The latter replicates the viral DNA and new viruses are formed. They are released into the medium by bursting the bacteria and the lytic cycle ends. Replication phenomena match very well a logistic growth of vimses, and we assume 

If replication begins at f = 0 and if we define t as the time elapsed from the adsorption to the replication of py /2 vimses, the solution of (8.32) reads 

We illustrate how to estimate the above parameters. The specific case we consider here is the interaction between the virus T7 and the bacterium Escherichia coli. The adsorption rate can be obtained by fitting g py) to experimental data [406] as shown in the inset of Fig. 8.2. The fit yields C = 1.39 x 10 ml and ki = (1.29 0.59) X 10 ml/min. The function (8.33) is called the one-step growth and is fitted to the experimental results [486] for replication of T7 inside E. coli. The fit, illustrated in the main part of Fig. 8.2, provides Y = 34.5, x = 18.4 min, and 2 = 1-39 min The kinetic equations for viruses, host bacteria, and infected bacteria can be written as 

The system (8.35) has four steady states we are interested in only two of them. The state (py, Pb i) = (0 Pb 0) i infection-free state which could represent an initial state, Pb(0) = Pb- Provided that T 1, this state is always unstable. 

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