Explaining the shape of a typical COVID 19 epidemic curve

Conversation
21

The passage below is taken from a publication by Sanford et al titled « Information Loss: Potential for Accelerating Natural Genetic Attenuation of RNA Viruses »

RNA viruses are excellent candidates for genetic degeneration because they

typically have an extraordinarily high mutation rate [14]. The higher mutation rate

of RNA viruses is a consequence of the novel mechanisms required for RNA

replication, which are especially prone to mutation, and the lack of effective repair

enzymes for RNA replication. Even in RNA viruses with relatively small genomes,

there appear to be as many as 0.1 to 1.0 new mutations per virus per replication

cycle [15]. The mutation rate in RNA viruses is so high that it becomes difficult

to speak of a given viral “strain”, because any genotype quickly mutates into a

complex of genotypes, such that any patient is soon infected with a “viral swarm”.

With such a high mutation rate, the large majority of viral genotypes in a patient

must carry many deleterious mutations, and so will be inferior to the original

infecting genotype. This implies the lack of a realistic mechanism to preserve a

“standard genotype”, and all RNA viral swarms should typically be on the verge

of mutational meltdown.

When a virus is transmitted from one individual to the next, the first individual

harbors a viral swarm. The second individual becomes infected by a random

subset of that swarm (conceivably a single genotype). With this type of bottleneck-

ing, the “best” viral genotypes within the first swarm have a small probability of

being transmitted to the next host. This probability becomes especially small when

infection arises from a single viral particle. Given a high mutation rate and regular

bottlenecks, the operation of Muller’s Ratchet becomes quite certain, which

should result in a continuous ratchet-like mutational degeneration of the viral

genome [6].

It seems to me that the logic of this passage is unassailable and therefore the conclusion that RNA viruses cannot escape slow erosion/natural attenuation is inescapable. Do you see what is wrong in this reasoning ?

For the record, here is the whole paper:
https://www.worldscientific.com/doi/pdf/10.1142/9789814508728_0015

22

I see a lot of bare assertions and very little logic.

First, you need to show the actual mutation rate for SARS-COV-2. Scientists are tracking how the viral genome is changing, so why don’t you find that info and present it?

Second, you need to show how less fit viruses would outcompete more fit viruses.

3 Likes
23

It doesn’t match reality. We see that RNA viruses do not erode.

1 Like
24

No, not at all a mysterious pattern. The numbers go up in the beginning because precautions have yet to be implemented or take full effect, then when they do, the numbers slowly turn around and go down, then as the country “opens up” again, restrictions are relaxed, and people become complacent, the numbers go up again.

This pattern makes perfect logical sense on the model where the virus shows no change in fitness, and what we are seeing is mostly a reflection of host societal response: Closing down likely centers of spread, implementing social distancing measures, wearing masks, washing hands, etc. This slows down the rate of spread of the virus. Then when more and more people stop following these rules, the virus starts spreading more and more quickly again.

1 Like
25

They made a nice video on this on Numberphile:

2 Likes
26

In fairness, it is mysterious to @Giltil. Doesn’t have to be though. This one is pretty straight forward.

3 Likes
27

Mysterious not only to me, but to Pr Didier Raoult also.

28

I understand. I highly recommend the video, where the curve is explained and reproduced easily simply by a relationship between the numbers of susceptible, infected, and recovered.

29

Nope. The overall shape of the curve is the same with or without precautions. See the Swedish example. Or see also the flu example.

30

Reference? Where can we find Raoult confused as to why a virus would spread more easily with an increase in social contact?

1 Like
31

But did you watch the video? You really should.

32

You’re right, sorry. What I should have said instead is that the flatness of the curve, as in how steeply it rises and tapers off again, is influenced by the strength and timing of the mitigating precautions taken.

The mere fact that it rises and then eventually tapers off again is not related to whether precautions are taken or not.

1 Like
34

This is a good answer to @Giltil question…
Thanks for posting it.

35

Is this the case?

COVID-19 Mortality by Country
COVID-19 Mortality by Country1920×1080 272 KB

I’ve charted daily mortality numbers for the 56 countries with the most total deaths reported to date. I represented the numbers as population rates so that the various countries could be compared on the same scale. Many European countries may follow that similar pattern, but many countries in other parts of the world do not. South American countries in particular seem to stand out as having different trends. And the US as noted also has a different pattern.

Data are from the COVID-19 Data Hub via the COVID19 R package.
Guidotti, E., Ardia, D., (2020), “COVID-19 Data Hub”, Journal of Open Source Software 5(51):2376, doi: 10.21105/joss.02376.

8 Likes
36

@AndyWalsh You made that??

I think I’m in love!! :wink: :heart: :laughing:

1 Like
37

I did. :blush:

Oh, and I should have added that I truncated the y axis because a handful of values were quite high and obscured most of the structure. Countries occasionally report cases with incomplete data all at once, resulting in those outliers.

2 Likes
38

In his article, Sanford provides several historical evidences of erosion of RNA viruses. See below:

Historical evidence that RNA viruses undergo natural genetic attenuation

Dengue type-2 virus ( DENV), a mosquito-borne, positive-sense, single-strand

RNA virus, caused an epidemic in several Pacific Islands from 1971 to 1974. A

recent paper [16] studied the epidemiological, clinical and biologic observations

recorded during this time. The authors note that the time period, population

dynamics and isolation of this epidemic gives a unique opportunity to study virus

evolution minus many confounding factors. The initial outbreak of the disease, on

Fiji and Tahiti, caused severe clinical symptoms, while the final outbreak on Tonga

produced mild symptoms and near-silent transmission. Sequence and phyloge-

netic analysis showed that the outbreaks were genetically related and all due to a

single introduction. Also these analyses placed the Tongan viral isolates in a single

clade, with some unique site substitutions compared to viral isolates early in the

epidemic. It is these deleterious genetic changes that Steel et al. [16] believe was

responsible for the reduced epidemic severity on Tonga in 1973/1974.

Severe acute respiratory syndrome ( SARS) caused by an animal-derived coro-

navirus appeared in the human population of Guangdong Province of China in late

2002. Sixty-one viral isolates from humans were sequenced from the early, middle

and late phases of the outbreak in this region and were compared to animal derived

viral sequences [17]. This epidemic was characterized by its sudden appearance,

its extreme virulence, its rapid spread, and the rapid collapse of the pandemic after

just two months [17]. This dramatic collapse cannot reasonably be attributed to

human intervention. Given that SARS in man appears to have an inordinately high

mutation rate of roughly 3 mutations per replication [18], and given that during

this very short-term pandemic 291 mutations accumulated in the virus, it seems

most reasonable to conclude that the outbreak ended prematurely because the

virus underwent mutational degeneration and natural genetic attenuation.

Similarly, Ebola outbreaks have emerged explosively, initially being extremely virulent and contagious, but very quickly they became self-contained apart from human intervention. While the Ebola virus appears to have an extremely wide host range, it has been almost impossible to find it in the natural fauna of the

relevant regions [19]. This can most reasonably be explained by self-containment

of the virus due to high mutation rates and natural genetic attenuation. Bowen

et al. [20] cite the World Health Organization’s report suggesting that such attenu-

ation occurred after just 10–11 passages within the human population.

Influenza A virus causes respiratory infections in mammals and birds. In

humans, this virus causes a yearly epidemic and an occasional pandemic. It

appears that influenza strains are continuously going extinct at a high rate. The

actual precursor strains of the H1N1 strain that caused the disastrous 1918 pan-

demic are unknown, and can be presumed to be extinct [i.e., 21, 22]. The H1N1

strain itself appears to have gone extinct in the mid-twentieth century, and appart

ently was inadvertently re-introduced from a researcher’s lab freezer in 1977 [23,

24]. During the 2009 H1N1 pandemic, one of two original strains went extinct

[25]. Given the global nature of influenza spread and distribution, it can very rea-

sonably be asked - why does the previous year’s strain of the flu routinely disap-

pear so quickly? Why do most strains of influenza appear to routinely go extinct?

The most reasonable answer would seem to be natural genetic attenuation due to

mutation accumulation.

Moreover, in addition to these historical evidences, there are also observational evidences from the current covid19 epidemic.

39

I’ve read somewhere that the mutation rate of SARS-COV-2 is about 1 mutation per genome per replication (Note that I’ve just tried to retrieve this info but without success so far).

This is clearly explained here: Explaining the shape of a typical COVID 19 epidemic curve - #21 by Giltil

40

It took me two minutes on google to find this: auspice

The mutation rate is about 23 substitutions per year

1 Like
41

The less virulent a virus is, the more effective it is, in fact the more functional it is. Usually that’s the case. Seems that you misunderstood virulence to be fitness…

2 Likes