How is the carrying capacity of a logistic growth model calculated?

Question

I am reading a book in epidemiology where the carrying capacity for a standard logistic growth rate is given by

K = (b - delta) / gamma

where:

K is the carrying capacity 
b is the birth rate 
delta is the death rate

but what is gamma?

Thank you

Answer 1

@Remi.b is correct that you haven't given us very much information, but I think we can reconstruct what's going on. Suppose the population growth rate is written out as

$$ \frac{dN}{dt} = N ( b - \delta - \gamma N) $$

then the equilibrium (carrying capacity) occurs when $N>0$ and $dN/dt=0$, i.e. $b - \delta - \gamma K = 0$. Solving this for $K$ gives $(b-\delta)/\gamma$ (as you stated).

So what is $\gamma$? It is the decrease in the per capita growth rate per unit of increase in population density, or more biologically speaking it's the decrease in the birth rate or the increase in the death rate per unit of increase in population density. This could be due to increased competition for resources, or decreased environmental quality, or attraction of predators, or ...

Another, vaguer way to say this would be to call it the "effect of density-dependence".

Given the equations you list in the comments, with a $-\gamma N$ term included in the per capita growth rate for each compartment ($S$, $E$, $I$), we can say more specifically that $\gamma$ determines the rate of density-dependent increase in the ("natural" or disease-independent) death rate per unit population density. This parameter would not typically be broken down into lower-level processes.