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Clarification on certain disease model parameters [message #635631] Wed, 27 October 2010 14:48 Go to next message
Traci Arthur-Hartranft is currently offline Traci Arthur-Hartranft
Messages: 9
Registered: August 2010
Junior Member
Hi - Can you help me with some clarification on specification of transmission rate and infectious mortality rate disease parameters?

Specifically, I think I was mistakenly always assuming the transmission rate for the disease input was basically the R0 value because most of the examples I saw for the STEM documentation were in the 1 to 2 range. But, if I understand right, you are actually looking for beta, from which R0 can be calculated as beta/gamma (transmission rate/recovery rate)? I just want to verify this because if I assume an R0 of 1.3 and a recovery rate of .175 (standard flu type parameters) I would want to enter a transmission rate of .23 which is much smaller than any of the disease Beta inputs I've seen as examples.

And I understand the units for recovery rates, incubation rates etc. as per day, with their relationship to the duration of infectiousness and the incubation period being clear. But I'm having a hard time with the infectious mortality rate. I'm finding that that is typically specified as # of deaths per 1000 individuals per year. Yours is in terms of population member/time period (i.e.,day)? Do we get this from something like the case fatality ratio?

Sorry for the remedial questions but I couldn't find specific documentation on this in the Help. My main concern is that, on our end, we enter a correct *transmission rate* and not a R0 value inappropriately.

Thanks - Traci
Re: Clarification on certain disease model parameters [message #635659 is a reply to message #635631] Wed, 27 October 2010 16:04 Go to previous messageGo to next message
Matthias Filter is currently offline Matthias Filter
Messages: 73
Registered: July 2009
Member
Hi Traci,

very good point! This somehow reminds me on a discussion we had some weeks ago on the possibility to use the dublin core structure to describe the meaning, units and possibly also the uncertainty connected with (all) parameter values. At that time a hierarchical dublin core structure was suggested (e.g. one general dublin core describing each disease parameter and if necessary a user specific dublin core that is attached to the parameters the user is providing which then overrides the general dublin core). As far as I got it this concept causes some performance problems within STEM, so I don't know wheather this might really be a path to follow.

Matthias
Re: Clarification on certain disease model parameters [message #635763 is a reply to message #635631] Thu, 28 October 2010 02:50 Go to previous messageGo to next message
James Kaufman is currently offline James Kaufman
Messages: 158
Registered: July 2009
Senior Member
Traci,
You are correct that the input in the disease wizard is for beta. R0 can be calculated as beta/gamma or beta/(gamma+birth rate). Units are determined by the time step (which is almost always 1 day but could be different). Ignoring births/deaths, if you want R0 of 1.3 with a recovery rate of .175 (per day) then transmission rate would be .23

Correct.... the units for recovery rates, incubation rates etc. are per day (same for infectious mortality).

The literature typically does report Ro not beta and mortality as # of deaths per 1000 individuals per year. We use fraction of population/time period because these are the actual coefficients used in the SIR or SEIR equations. It should be relatively easy to convert between the two. In the case of mortality we just need to calculate #deaths/#cases to get the fraction. Then multiply by gamma to get the cases per day.

Thank you for this comment! We need to improve the context sensitive help to make this really clear to all users. Per Matthias' comment on the call today we should probably store the units somehow in the decorators xml or the dublin core (we need to look at the best way to do this without breaking things....)

Best Regards,
Jamie
Re: Clarification on certain disease model parameters [message #635765 is a reply to message #635631] Thu, 28 October 2010 02:53 Go to previous messageGo to next message
James Kaufman is currently offline James Kaufman
Messages: 158
Registered: July 2009
Senior Member
Traci,
Here is another idea. How about if we add to the wizard a field that shows the user the Ro value corresponding to the beta and gamma values used? This could just be a label we update in the wizard (but it should make it obvious the entry parameter is beta).
What do you think?
Best Regards,
Jamie
Re: Clarification on certain disease model parameters [message #636341 is a reply to message #635763] Sun, 31 October 2010 07:13 Go to previous messageGo to next message
Arik Kershenbaum is currently offline Arik Kershenbaum
Messages: 13
Registered: January 2010
Location: Israel
Junior Member
Hi,

Sorry if I've misunderstood what you're saying, but your definition of R0 seems a little mixed up.

R0 is the number of newly infected individuals that a single infected individual would generate over its infective lifetime in a wholly susceptible population- i.e. the numer of new cases that each old case replaces itself with. That is why if R0>1 then the disease spreads, otherwise it dies out.

Note:
1) R0 is a ratio; it has no units, so it is independent of the time step.
2) If the recover rate is 0.175 per day, then an individual is infectious for on average 1/0.175=5.7 days. If the transmission rate (beta) is 0.23, then over that time, they will infect 5.7*0.23 of the susceptible individuals that they come into contact with each day. R0 is dependent on the number of contacts, and cannot be defined by disease parameters alone. If they mix with 10 new (i.e. susceptible) people every day, they will infect 5.7*0.23*10=13 before recovering, i.e. R0=13 - this is a very contagious disease. But if they sneeze on just one person every other day, the R0=5.7*0.23*0.5=0.66 - the disease will not persist.
Clearly, as the number of susceptibles falls, the number of new cases falls, so R0 is only really of significance right at the start of an epidemic.

Arik


==============
Arik Kershenbaum
Prof Blaustein's laboratory
Department of Evolutionary and Environmental Biology
University of Haifa
http://research.haifa.ac.il/~leon/html/Arik_Page.htm
Re: Clarification on certain disease model parameters [message #636459 is a reply to message #635631] Mon, 01 November 2010 13:00 Go to previous messageGo to next message
Traci Arthur-Hartranft is currently offline Traci Arthur-Hartranft
Messages: 9
Registered: August 2010
Junior Member
Jamie - I think the suggestion to show the resulting Ro in the wizard is a good one. It would clarify the input parameters, as well as help a user to verify that their inputs are doing what they expect.

Arik - Thanks for bringing mixing into the actual application of these parameters.

Traci
Re: Clarification on certain disease model parameters [message #636570 is a reply to message #635631] Mon, 01 November 2010 22:44 Go to previous messageGo to next message
Stefan Edlund is currently offline Stefan Edlund
Messages: 127
Registered: July 2009
Location: IBM
Senior Member
Adding R0 to the wizard is pretty straightforward. As long as the user understands that a value of R0 > 1 does not necessarily mean that the disease won't become extinct, especially if:

1. There's an inoculator that inoculates the population initially.
2. The background birth rate / death rate of the population is > 0.

Regards,
/ Stefan
Re: Clarification on certain disease model parameters [message #637254 is a reply to message #636341] Thu, 04 November 2010 17:47 Go to previous message
James Kaufman is currently offline James Kaufman
Messages: 158
Registered: July 2009
Senior Member
Arik,
You are correct, the equation above only holds for if the fraction of the population that is susceptible, s==1.

In general R<sub>o</sub>~s&beta;/(&gamma; + &mu;)
This is actually problematic to show in the wizard as we do not have 's'. We can try to get it from the innoculators/infectors but users will likely create the disease before creating them. This would create more questions than it answers. Instead, I updated the context sensitive help on the Disease Wizard explaining the difference between &beta. and R<sub>o</sub>. To see the new help, get latest and create a new disease. Click the question mark then select the link to Disease Wizard Help.

see also:
http://wiki.eclipse.org/Introduction_to_Compartment_Models
and
http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology

[Updated on: Thu, 04 November 2010 17:50]

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