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Spatial associations invalidate mass action assumptions.
Under mass action assumptions, the dynamics would be identical to Eq. (1) A ˙ = gS (N - A ) - δXA, in which N= R+ A is the total concentration of inactive plus active reactant molecules and, in this case, we write the back reaction rate as δ X rather than just δ as in the earlier equation.
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A small radius corresponds to a spatially structured system while larger radii converge to a mass action assumption.
Alternatively, some studies assume that chemical kinetics depart from the classical mass action assumption (Table 2).
We notice that the prediction holds for an effectively infinite population under the mass action assumption.
This corresponds to the island model in the populations genetics literature and mass action assumption in epidemiological models.
I used the Smoldyn simulation package to study reaction dynamics when the mass action assumption does not hold.
The force of infection (ignoring transmission via movements) is not a linear function of the number of infected farms (contrasting with the standard mass action assumption).
The mass action assumption, which goes back to the pioneering work of Kermak and McKendrick [ 34], has almost always been used for transmission in host-pathogen models, in some cases, non-critically.
The high precision of classical chemical kinetics arises because the mass action assumption implies that infinitesimal changes in input concentration are instantly translated into a linear change in the rate of collisions between potential reactants.
The basal death rate is b0 and the population's size is density-regulated in a linear manner according to a standard mass action assumption [ 53] with a density coefficient of s such that the total death rate is b0+ sH.
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