Gomes - Revision history

Alex: /* About */

2021-07-23T02:11:04Z

About

← Older revision		Revision as of 20:11, 22 July 2021
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	As of 3 December 2020, one of the authors has [https://twitter.com/mgmgomes1/status/1334572853056983043 reaffirmed her belief in a HIT of around 20%].		As of 3 December 2020, one of the authors has [https://twitter.com/mgmgomes1/status/1334572853056983043 reaffirmed her belief in a HIT of around 20%].

	'''Additional note''': To summarise the main objection to the paper, it hinges on there being a wide variation in ''susceptibility'' (propensity to catch the disease), but the existence of superspreaders (people who transmit the disease a lot more than average) only proves there is a wide variation in ''transmissibility''. Unless superspreaders are also supercatchers, there is no reason to expect them to be preferentially removed from the susceptible pool, which means the existence of superspreaders alone gives no reason to expect a lower HIT by this mechanism. So the evidence for superspreaders (which is fairly solid) only becomes evidence for this low-HIT mechanism if superspreaders arise because they are generally more sociable (in which case you'd expect them to catch the disease more) ~~or because~~ they are just emitting more (or more potent) viral particles. Since we don't know a priori (at least, as of May 2020) which of these is true, it becomes an empirical question - it can only be decided by observation, not just mathematics, and as far as I can see, observation has come down on the side of a HIT that is not a great deal lower than the naive $$1-1/R_0$$.		'''Additional note''': To summarise the main objection to the paper, its mechanism hinges on there being a wide variation in ''susceptibility'' (propensity to catch the disease), but the existence of superspreaders (people who transmit the disease a lot more than average) only proves there is a wide variation in ''transmissibility''. Unless superspreaders are also supercatchers, there is no reason to expect them to be preferentially removed from the susceptible pool, which means the existence of superspreaders alone gives no reason to expect a lower HIT by this mechanism. So the evidence for superspreaders (which is fairly solid) only becomes evidence for this low-HIT mechanism if superspreaders arise because they are generally more sociable (in which case you'd expect them to catch the disease more), not if they are just emitting more (or more potent) viral particles. Since we don't know a priori (at least, as of May 2020) which of these is true, it becomes an empirical question - it can only be decided by observation, not just mathematics, and as far as I can see, observation has come down on the side of a HIT that is not a great deal lower than the naive $$1-1/R_0$$.
	</blockquote>		</blockquote>

Alex: /* About */

2021-07-23T00:14:58Z

About

← Older revision		Revision as of 18:14, 22 July 2021
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	As of 3 December 2020, one of the authors has [https://twitter.com/mgmgomes1/status/1334572853056983043 reaffirmed her belief in a HIT of around 20%].		As of 3 December 2020, one of the authors has [https://twitter.com/mgmgomes1/status/1334572853056983043 reaffirmed her belief in a HIT of around 20%].

			'''Additional note''': To summarise the main objection to the paper, it hinges on there being a wide variation in ''susceptibility'' (propensity to catch the disease), but the existence of superspreaders (people who transmit the disease a lot more than average) only proves there is a wide variation in ''transmissibility''. Unless superspreaders are also supercatchers, there is no reason to expect them to be preferentially removed from the susceptible pool, which means the existence of superspreaders alone gives no reason to expect a lower HIT by this mechanism. So the evidence for superspreaders (which is fairly solid) only becomes evidence for this low-HIT mechanism if superspreaders arise because they are generally more sociable (in which case you'd expect them to catch the disease more) or because they are just emitting more (or more potent) viral particles. Since we don't know a priori (at least, as of May 2020) which of these is true, it becomes an empirical question - it can only be decided by observation, not just mathematics, and as far as I can see, observation has come down on the side of a HIT that is not a great deal lower than the naive $$1-1/R_0$$.
	</blockquote>		</blockquote>

Alex: /* About */

2020-12-10T09:34:48Z

About

← Older revision		Revision as of 03:34, 10 December 2020
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	Since then, these authors and others have published [https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v3 a new paper] (Aguas et al, November 2020) seeking to deduce HITs for European countries by fitting their model to case numbers, using certain values for the level of NPIs (non-pharmaceutical interventions, disease suppression by distancing, hygiene, stay-at-home etc.). They conclude that the HITs for the studied countries are around 10-20%, which I do not find believable for the reasons given above (and others). There is [https://www.medrxiv.org/content/10.1101/2020.12.01.20242289v1 a paper] (Fox et al, December 2020) which reanalyses Aguas et al using different assumptions (which I find more persuasive) about the suppression levels, and arrives at estimates of 60-80% for HITs. The key difference is that Aguas et al assumes that suppression measures have had no effect in Europe since August 2020, whereas Fox et al assumes that there has been fairly strong suppression all the time since March 2020.		Since then, these authors and others have published [https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v3 a new paper] (Aguas et al, November 2020) seeking to deduce HITs for European countries by fitting their model to case numbers, using certain values for the level of NPIs (non-pharmaceutical interventions, disease suppression by distancing, hygiene, stay-at-home etc.). They conclude that the HITs for the studied countries are around 10-20%, which I do not find believable for the reasons given above (and others). There is [https://www.medrxiv.org/content/10.1101/2020.12.01.20242289v1 a paper] (Fox et al, December 2020) which reanalyses Aguas et al using different assumptions (which I find more persuasive) about the suppression levels, and arrives at estimates of 60-80% for HITs. The key difference is that Aguas et al assumes that suppression measures have had no effect in Europe since August 2020, whereas Fox et al assumes that there has been fairly strong suppression all the time since March 2020.

	As of 3 December 2020, one of the authors has [https://twitter.com/mgmgomes1/status/1334572853056983043 reaffirmed her belief in a HIT of around 20%]. ~~(For what it's worth, my personal guess would be for infection-acquired HITs of around 60-70%.)~~		As of 3 December 2020, one of the authors has [https://twitter.com/mgmgomes1/status/1334572853056983043 reaffirmed her belief in a HIT of around 20%].
	</blockquote>		</blockquote>

Alex: /* About */

2020-12-09T22:34:35Z

About

← Older revision		Revision as of 16:34, 9 December 2020
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	The post below was written on 22 May 2020. This boxed comment is written from a later perspective (5 December 2020), and slightly more opinionated than the post from May which was intended to be neutral in tone.		The post below was written on 22 May 2020. This boxed comment is written from a later perspective (5 December 2020), and slightly more opinionated than the post from May which was intended to be neutral in tone.

	At the time of writing the post, such low HITs seemed rather unlikely (to me anyway) based on the dynamics of the first waves around the world, but now I believe the evidence is almost conclusive that such low HITs are impossible. We have had second waves in places with high attack rates from a previous first wave. For example, New York City is now experiencing [https://www.nytimes.com/interactive/2020/nyregion/new-york-city-coronavirus-cases.html a resurgence] despite [https://www.nbcnewyork.com/news/local/cuomo-outlines-reopening-roadmap-for-new-york-as-daily-deaths-hit-lowest-level-in-weeks/2390949/ an estimated 24.7%] having been infected by late April, and despite [https://www.bbc.co.uk/news/world-us-canada-54906483 ongoing suppression measures], together suggesting the HIT is well about 25% for NYC. There is a similar story in London and other places. It's possible to imagine an argument that the HIT is as low as 25% in NYC though it would be quite strained, relying on assuming the present restrictions are having no suppressive effect at all, and the outbreaks are happening in different areas from before. It seems to me more likely that the HIT for NYC is considerably higher.		At the time of writing the post, such low HITs seemed rather unlikely (to me anyway) based on the dynamics of the first waves around the world, but now I believe the evidence is almost conclusive that such low HITs are impossible. We have had second waves in places with high attack rates from a previous first wave. For example, New York City is now experiencing [https://www.nytimes.com/interactive/2020/nyregion/new-york-city-coronavirus-cases.html a resurgence] despite [https://www.nbcnewyork.com/news/local/cuomo-outlines-reopening-roadmap-for-new-york-as-daily-deaths-hit-lowest-level-in-weeks/2390949/ an estimated 24.7%] having been infected by late April, and despite [https://www.bbc.co.uk/news/world-us-canada-54906483 ongoing suppression measures], together suggesting the HIT is well about 25% for NYC. There is a similar story in London, Stockholm and other places. It's possible to imagine an argument that the HIT is as low as 25% in NYC though it would be quite strained, relying on assuming the present restrictions are having no suppressive effect at all, and the outbreaks are happening in different areas from before. It seems to me more likely that the HIT for NYC is considerably higher.

	Since the May 2020 paper, two of the original authors have published [https://arxiv.org/abs/2008.00098 a new paper] with a more streamlined presentation of their argument where they find the analytic formula noted in the appendix of the post below.		Since the May 2020 paper, two of the original authors have published [https://arxiv.org/abs/2008.00098 a new paper] with a more streamlined presentation of their argument where they find the analytic formula noted in the appendix of the post below.
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	Since then, these authors and others have published [https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v3 a new paper] (Aguas et al, November 2020) seeking to deduce HITs for European countries by fitting their model to case numbers, using certain values for the level of NPIs (non-pharmaceutical interventions, disease suppression by distancing, hygiene, stay-at-home etc.). They conclude that the HITs for the studied countries are around 10-20%, which I do not find believable for the reasons given above (and others). There is [https://www.medrxiv.org/content/10.1101/2020.12.01.20242289v1 a paper] (Fox et al, December 2020) which reanalyses Aguas et al using different assumptions (which I find more persuasive) about the suppression levels, and arrives at estimates of 60-80% for HITs. The key difference is that Aguas et al assumes that suppression measures have had no effect in Europe since August 2020, whereas Fox et al assumes that there has been fairly strong suppression all the time since March 2020.		Since then, these authors and others have published [https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v3 a new paper] (Aguas et al, November 2020) seeking to deduce HITs for European countries by fitting their model to case numbers, using certain values for the level of NPIs (non-pharmaceutical interventions, disease suppression by distancing, hygiene, stay-at-home etc.). They conclude that the HITs for the studied countries are around 10-20%, which I do not find believable for the reasons given above (and others). There is [https://www.medrxiv.org/content/10.1101/2020.12.01.20242289v1 a paper] (Fox et al, December 2020) which reanalyses Aguas et al using different assumptions (which I find more persuasive) about the suppression levels, and arrives at estimates of 60-80% for HITs. The key difference is that Aguas et al assumes that suppression measures have had no effect in Europe since August 2020, whereas Fox et al assumes that there has been fairly strong suppression all the time since March 2020.

	As of 3 December 2020, one of the authors has [https://twitter.com/mgmgomes1/status/1334572853056983043 reaffirmed her belief in a HIT of around 20%]. (For what it's worth, my personal guess would be for infection-acquired HITs of around 60%.)		As of 3 December 2020, one of the authors has [https://twitter.com/mgmgomes1/status/1334572853056983043 reaffirmed her belief in a HIT of around 20%]. (For what it's worth, my personal guess would be for infection-acquired HITs of around 60-70%.)
	</blockquote>		</blockquote>

Alex: /* About */

2020-12-05T20:36:09Z

About

← Older revision		Revision as of 14:36, 5 December 2020
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	Since then, these authors and others have published [https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v3 a new paper] (Aguas et al, November 2020) seeking to deduce HITs for European countries by fitting their model to case numbers, using certain values for the level of NPIs (non-pharmaceutical interventions, disease suppression by distancing, hygiene, stay-at-home etc.). They conclude that the HITs for the studied countries are around 10-20%, which I do not find believable for the reasons given above (and others). There is [https://www.medrxiv.org/content/10.1101/2020.12.01.20242289v1 a paper] (Fox et al, December 2020) which reanalyses Aguas et al using different assumptions (which I find more persuasive) about the suppression levels, and arrives at estimates of 60-80% for HITs. The key difference is that Aguas et al assumes that suppression measures have had no effect in Europe since August 2020, whereas Fox et al assumes that there has been fairly strong suppression all the time since March 2020.		Since then, these authors and others have published [https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v3 a new paper] (Aguas et al, November 2020) seeking to deduce HITs for European countries by fitting their model to case numbers, using certain values for the level of NPIs (non-pharmaceutical interventions, disease suppression by distancing, hygiene, stay-at-home etc.). They conclude that the HITs for the studied countries are around 10-20%, which I do not find believable for the reasons given above (and others). There is [https://www.medrxiv.org/content/10.1101/2020.12.01.20242289v1 a paper] (Fox et al, December 2020) which reanalyses Aguas et al using different assumptions (which I find more persuasive) about the suppression levels, and arrives at estimates of 60-80% for HITs. The key difference is that Aguas et al assumes that suppression measures have had no effect in Europe since August 2020, whereas Fox et al assumes that there has been fairly strong suppression all the time since March 2020.

	As of 3 December 2020, one of the authors has [https://twitter.com/mgmgomes1/status/1334572853056983043 reaffirmed her belief in a HIT of around 20%]. (For what it's worth, my personal guess would be for HITs of around 60%.)		As of 3 December 2020, one of the authors has [https://twitter.com/mgmgomes1/status/1334572853056983043 reaffirmed her belief in a HIT of around 20%]. (For what it's worth, my personal guess would be for infection-acquired HITs of around 60%.)
	</blockquote>		</blockquote>

Alex: /* About */

2020-12-05T17:52:02Z

About

← Older revision		Revision as of 11:52, 5 December 2020
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	[[Main_Page\|Back to main page]]		[[Main_Page\|Back to main page]]

			<blockquote style="background-color: #ececec; padding: 10px; border:solid thin grey">
			The post below was written on 22 May 2020. This boxed comment is written from a later perspective (5 December 2020), and slightly more opinionated than the post from May which was intended to be neutral in tone.

			At the time of writing the post, such low HITs seemed rather unlikely (to me anyway) based on the dynamics of the first waves around the world, but now I believe the evidence is almost conclusive that such low HITs are impossible. We have had second waves in places with high attack rates from a previous first wave. For example, New York City is now experiencing [https://www.nytimes.com/interactive/2020/nyregion/new-york-city-coronavirus-cases.html a resurgence] despite [https://www.nbcnewyork.com/news/local/cuomo-outlines-reopening-roadmap-for-new-york-as-daily-deaths-hit-lowest-level-in-weeks/2390949/ an estimated 24.7%] having been infected by late April, and despite [https://www.bbc.co.uk/news/world-us-canada-54906483 ongoing suppression measures], together suggesting the HIT is well about 25% for NYC. There is a similar story in London and other places. It's possible to imagine an argument that the HIT is as low as 25% in NYC though it would be quite strained, relying on assuming the present restrictions are having no suppressive effect at all, and the outbreaks are happening in different areas from before. It seems to me more likely that the HIT for NYC is considerably higher.

			Since the May 2020 paper, two of the original authors have published [https://arxiv.org/abs/2008.00098 a new paper] with a more streamlined presentation of their argument where they find the analytic formula noted in the appendix of the post below.

			Since then, these authors and others have published [https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v3 a new paper] (Aguas et al, November 2020) seeking to deduce HITs for European countries by fitting their model to case numbers, using certain values for the level of NPIs (non-pharmaceutical interventions, disease suppression by distancing, hygiene, stay-at-home etc.). They conclude that the HITs for the studied countries are around 10-20%, which I do not find believable for the reasons given above (and others). There is [https://www.medrxiv.org/content/10.1101/2020.12.01.20242289v1 a paper] (Fox et al, December 2020) which reanalyses Aguas et al using different assumptions (which I find more persuasive) about the suppression levels, and arrives at estimates of 60-80% for HITs. The key difference is that Aguas et al assumes that suppression measures have had no effect in Europe since August 2020, whereas Fox et al assumes that there has been fairly strong suppression all the time since March 2020.

			As of 3 December 2020, one of the authors has [https://twitter.com/mgmgomes1/status/1334572853056983043 reaffirmed her belief in a HIT of around 20%]. (For what it's worth, my personal guess would be for HITs of around 60%.)
			</blockquote>

	= Article =		= Article =

Alex at 12:28, 5 December 2020

2020-12-05T12:28:16Z

← Older revision		Revision as of 06:28, 5 December 2020
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			= About =

			[[Main_Page\|Back to main page]]

	= Article =		= Article =

Alex: /* Appendix - direct formulae */

2020-06-07T04:23:26Z

Appendix - direct formulae

← Older revision		Revision as of 22:23, 6 June 2020
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	As it happens, there is a nice clean procedure to directly calculate the HIT under the authors' model, so there is no need for simulation, and there is no dependency of on particular characteristics such as the timing of the switching on and off of social distancing. (The reason for this is that $$S_t(x)=S_0(x)e^{-\Lambda(t)x}$$. That is, the $$t-$$dependence and $$x-$$dependence decouple.) I don't think the authors used this.		As it happens, there is a nice clean procedure to directly calculate the HIT under the authors' model, so there is no need for simulation, and there is no dependency of on particular characteristics such as the timing of the switching on and off of social distancing. (The reason for this is that $$S_t(x)=S_0(x)e^{-\Lambda(t)x}$$. That is, the $$t-$$dependence and $$x-$$dependence decouple.) I don't think the authors used this.

	For the Gamma family there happens to be a closed-form formula. Using the "susceptibility" model it's		For the Gamma family there even happens to be a completely closed-form formula. Using the "susceptibility" model it's

	\[\text{HIT} = 1-R_0^{-(1+CV^2)^{-1}},\] and with the "connectivity" model it's		\[\text{HIT} = 1-R_0^{-(1+CV^2)^{-1}},\] and with the "connectivity" model it's

Alex at 04:22, 7 June 2020

2020-06-07T04:22:56Z

← Older revision		Revision as of 22:22, 6 June 2020
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	This paper made a media splash early in May 2020 with		This paper made a media splash early in May 2020 with
	[https://www.spectator.co.uk/article/herd-immunity-may-only-need-a-10-per-cent-infection-rate headlines] such as "Herd immunity may only need 10-20 per cent of people to be infected". The proposed mechanism is that people who are more susceptible to the infection are those more involved in spreading it, but will also become immune at a faster rate than others, so the disease naturally tends to make the key players immune more so than others.		[https://www.spectator.co.uk/article/herd-immunity-may-only-need-a-10-per-cent-infection-rate headlines] such as "Herd immunity may only need 10-20 per cent of people to be infected". The proposed mechanism is that people who are more susceptible to the infection are those more involved in spreading it, but will also become immune at a faster rate than others, so the disease naturally tends to make the key players immune more so than others.

			= Summary =
			(Opinion-based) I believe that studying heterogeneities will be important because the herd immunity threshold may indeed be lower than the simplistically-calculated value, and I also believe that the Gomes model is a potentially useful way to introduce heterogeneities that could be applied in general as a meta-method to more realistic/non-toy models. However, for reasons given below, I believe that the actual numerical results in this paper can only be taken as illustrative and should not be taken as representing reality.

	= Discussion =		= Discussion =

Alex: /* Discussion */

2020-05-22T16:20:54Z

Discussion

← Older revision		Revision as of 10:20, 22 May 2020
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	* There is actually a nice clean way to evaluate the HIT directly from the susceptibility distribution under the given models.		* There is actually a nice clean way to evaluate the HIT directly from the susceptibility distribution under the given models.

			* In their model, social distancing / locking down only affects the overall time parameter. It's unclear how realistic this is, but under this model one could decouple the question of what the HIT is, with how to manage (by distancing etc.) the flow of the disease. As such, the focus is mainly on what the HIT is.

	* The present paper shows what happens if you "artificially" add in a variation in susceptibility, i.e., treat everyone uniformly except for a susceptibility parameter controlled by a given distribution. An alternative approach would be to use a real life contact graph, or some version of it. Age- and location-based contact information have been studied for this purpose, e.g., [https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005697 Prem et al] and [https://www.sciencedirect.com/science/article/pii/S1755436518300306 Klepac et al]. Such a calculation is carried out in [https://arxiv.org/abs/2005.03085 Bitton et al] using Age- and Activity-based mixing matrices. They find, inter alia, that if $$R_0=3$$ then the HIT is reduced from $$66.7%$$ to $$49.1%$$. This empirically-derived distribution has the merit of being justifiable, but (and I'm speculating here) I wonder if it understates the full heterogeneity, in which case there might be an argument for trying a hybrid method where you artificially introduce a little more variability (somehow calibrated to reality), maybe in the manner of the present paper, on top of the empirically-found mixing matrices.		* The present paper shows what happens if you "artificially" add in a variation in susceptibility, i.e., treat everyone uniformly except for a susceptibility parameter controlled by a given distribution. An alternative approach would be to use a real life contact graph, or some version of it. Age- and location-based contact information have been studied for this purpose, e.g., [https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005697 Prem et al] and [https://www.sciencedirect.com/science/article/pii/S1755436518300306 Klepac et al]. Such a calculation is carried out in [https://arxiv.org/abs/2005.03085 Bitton et al] using Age- and Activity-based mixing matrices. They find, inter alia, that if $$R_0=3$$ then the HIT is reduced from $$66.7%$$ to $$49.1%$$. This empirically-derived distribution has the merit of being justifiable, but (and I'm speculating here) I wonder if it understates the full heterogeneity, in which case there might be an argument for trying a hybrid method where you artificially introduce a little more variability (somehow calibrated to reality), maybe in the manner of the present paper, on top of the empirically-found mixing matrices.