The models are based on a single reproduction number.
It means that everyone who is not yet infected is about equally susceptible of becoming infected under the same external circumstances.
I doubt this assumption is really true for covid-19.
I think the likelihood of becoming infected also depends on the characteristics of the individual person itself (age, sex, genetics and even behaviour) and might differ a lot between different categories of the population.
This is important for these models - as in that case they give a too pessimistic view.
Are there no more advanced models taking the difference in "susceptibility" into account
and if so what are the indicative parameter values for COVID for these models ?
Do you mean that they do not take account of the fact that the number of susceptible people will go down due to the fact that a certain percentage of the population has already had the disease?
Since the percentage that have had it is still small then I doubt if it is a significant factor at the moment.
No, I didn't mean that. The number of susceptible people indeed goes down once you have the disease (that assumption is OK for me although some are debating if you really get lifelong immunity once you have contracted the virus but that is another discussion).
Not necessarily. To make it clear by an extreme example to make the point clear.
Suppose:
20% of the population is very susceptible for the virus and
80% of the population (due to age, genetic, behaviour) has a very high "resistance" against the virus. So it is very hard to infect people in this group.
Under this supposition, the virus will very rapidly spread under the 20% group and will only infect a very small number of the 80% group. Once the virus has infected most of the 20% group then it will quickly go down as the 20% group has immunity and the 80% group has a high resistance. So in this case only about 20% of the population will be infected while the simple models would predict that 90% or more would become infected.
So actually the answer to my first question is almost yes, it is the the fact that r will go down as the number of susceptible people goes down that you are concerned about, but with the additional factor that possibly only a small percentage of the population is susceptible (or strongly susceptible anyway). I would have thought that the models would include some adjustment for this, but I don't know.
No, the models don't take this into account.
They work with the parameter R0 = basic reproduction number which is considered constant over time.
The effective reproduction number is a different metric which declines over time when more and more people become immune. I was not referring to this metric.
To model my example of the 2 very distinct groups you would need 4 basic reproduction numbers:
basic reproduction number for a population only consisting of the 20% group (this R0 will be high - e.g. 5)
basic reproduction number for a population only consisting of the 80% group (this R0 will be small - e.g. less than 1)
basic reproduction number of a person in the 20% group to persons in 80% group (of course you could simplify this and assume that this is the same as 2.)
basic reproduction number of a person in the 80% group to persons in 20% group (you could simplify this and assume that this one is equal to 1.)
Sorry to be coming back late to this discussion. I'll try to comment on both @janvda's and @Colin's posts.
Yes, just one reproduction number at any one time. At t = 0, when the whole population is susceptible, the reproduction number is R0. At later times, it is Re = R0 * s, where s is the susceptible fraction of the population.
There a lots of advanced models, but none I would try to implement in Node-RED . It is usual to think of Re as equal to the number of "effective" (infection-producing) contacts an infected person has each day, multiplied by the number of days he/she remains infected. More sophisticated models sometimes use a distribution of values for Re, reflecting the idea that some individuals may be more infectious, either because they shed more virus, have more contacts, or remain infectious for longer. Also, some individuals may be more susceptible than the rest, increasing the number of effective contacts. (Conversely, for fewer effective contacts.) If the distributions of these properties can be assumed to be normal (gaussian), then Re is just described by a mean value and variance, and the effect is relatively easy to propagate through the model. If any of the distributions is skewed or discontinuous, there can be difficulty.
This is not a problem for the model. If the 80% is totally resistant, then s = 0.2 and Re = 0.2 * R0. It is very likely that Re < 1, and the infection will not spread. If the 80% is only 10 times less likely than the rest to contract the disease, then a contact with a resistant individual counts as 1/10th of a contact, and effectively s = 0.28. This kind of reasoning applies to any kind of immunity, complete or partial, whether intrinsic or acquired from vaccination or convalescence. Unfortunately, the data for COVID-19 does not seem to support the idea of any significant degree of natural immunity.
. It is usual to think of Re as equal to the number of "effective" (infection-producing) contacts an infected person has each day, multiplied by the number of days he/she remains infected. More sophisticated models sometimes use a distribution of values for Re, reflecting the idea that some individuals may be more infectious, either because they shed more virus, have more contacts, or remain infectious for longer. Also, some individuals may be more susceptible than the rest, increasing the number of effective contacts. (Conversely, for fewer effective contacts.) If the distributions of these properties can be assumed to be normal (gaussian), then Re is just described by a mean value and variance, and the effect is relatively easy to propagate through the model. If any of the distributions is skewed or discontinuous, there can be difficulty.