Disaggregated SIR model from The SD forum

[LAUJJL]

Hi Jim

joined the disaggregated Sir model from the Sidmode1 model from Business dynamics.
Regards.
Jean-Jacques Laublé

[LAUJJL]

Hi Jim

Here is an amelioration from the first model.

But the problem is that I can calculate the number of contact with two different ways. And both do not deliver the same results. I have too different infectivities values.
One solution gives a constant number of contacts and average infectivity, and the other not.
The constant value for the number of contact corresponds to your formula.

But when one applies the constant infectivity to a population of 10000 children and no adults, the result is not the same!
I join the model and leave it for some days later on.
There must be some explanations.
Regards.
JJ

[LAUJJL]

Hi Jim

I made probably several mistakes in the previous model, and I did not calculate properly the contact number that needs some integration instead of merely multiplying by the duration. But I do not see yet a way to calculate it in this case. The infectivity that is variable is correct.
I used the avrage infctivity to recalculate the three stocks in the lower part of the model, and the aggregated results correspond to the additions of the disaggregated ones.
For instance infectious population I is equal to infectious population.
I will think later on at the contact number problem.
I wonder if it has a meaning in the case of the disaggregated model.
I had not the time to consult your references. No time!
Joined the third model, with only the calculation of the infectivity and the verification that it is correct. A kind of mass balance.
Regards.
JJ

[LAUJJL]

Hi Jim

I think that now I have understood the problem.
I join a last model, I hope, that summarizes the problem.

In my previous model, I calculated a variable infectivity that in fact does not correspond to anything real. Besides its value changes when one changes some parameters that should not influence it. It is too influenced by the susceptible population, that is non sense.
In fact it is a variable infectivity that matches exactly the working of the disaggregated model, but in an aggregated way, but that match works only for the parameters of the situation.

I have looked back at the sirmode2 model, and understood that the infectivity constant is the right one.
But one must first calculate the contact number before calculating the infectivity aggregated, and one can do it because the infectious contacts per day per person infected is constant, which can the be multiplied by the average duration.
One gets then the weighted average infectivity which is equal to your formula.
But one must be aware that this weighted infectivity is not usable in an aggregated model, because if you replace the opportunistic infectivity by the weighted infectivity the results will not be the same as in the disaggregated model.
This is quite evident, because the weighted infectivity does not give any information about the real infectivities of Adult and Child that is needed.
Interesting problem!
Best regards.
JJ