R0 (basic reproduction number for a disease) is a fiction. It does not exist!
R0 is what mathematicians figure out based on the shape of the epidemic curve. If every person infected infects N other people, then you get the curve from the equation. It’s equation fitting. And bluntly put, it’s meaningless nonsense but keeps getting repeated. In the modern world it should be discarded! This diagram to the left shows a real-world scale-free network, the internet. This diagram communicates the concept of how diseases spread far, far better.
In the real world, infections transmit by what is best described as scale-free networks. Each person has a different network of contacts. Some can infect many. Most infect a few, or none at all. Time is a factor, because infecting nodes recover, cannot become nodes again, or they die, and then that node’s contact network is usually gone.
Super-spreaders of infection are key. In the real world, there is a huge spread of R numbers for individuals. The SARS epidemic developed the first known dataset where virtually every contact was traced for every person who got sick. What this dataset showed is that if you identify the super-spreaders who may infect tens or hundreds of people and stop them, you will contain the disease [1]. This work by Lloyd-Smith, Schrieber, Kopp, and Getz should be the basis of epidemic response. Trace all contacts. Identify the source. Quarantine or treat. Repeat.
And most of all — identify who could be a superspreader. Some examples: A ticket seller. A priest giving communion. A prostitute. All of those could have many contacts that could spread infection. People in positions to spread the illness should either stop the behavior that would spread the disease, or else take precautions that will prevent transmission if the function is important enough.
Contact, direct or indirect is required for infection. This can be hand to hand, coughing directly in the area others are present, or leaving it on a surfce (and sometimes carried by an insect or animal). [Update: all it takes is breathing, no coughing required for CSARS-COVID-19.] Infectious disease of this enveloped respiratory virus kind propagates through people who are the agents. When a person dies, their links to their personal network end. And when a person recovers, they are no longer capable of becoming an infectious carrier, so the link the disease has to their network ends. So as the disease progresses, it loses its ability to find new infectees.
About 70% of the population getting infected because of recovery or death is a pretty consistent result that epidemologists see with diseases like influenza. The Epiflex [2] simulator is an agent model system that simulates human movement and mixing with infectious organisms. It can be downloaded and a pre-defined model can be run, and tweaks can be made to the model to see what happens. (I can also provide a later version than the one provided in supporting data. The later version has a lot more detail data available as output. Write to me at: author of this paper.)
Intuitive paradoxes happen in epidemics. First, smaller groups will see higher infection rates because a larger proportion of the group can be contacted before the first people either die or recover. If it is small enough, everyone will be contacted. There was an island in the South Pacific with an approximate 700 person population that was reported to have had everyone wiped out from influenza during WWII. In 1917–18’s epidemic, there was a barely contacted village in North America that had 50% total population loss from the flu. This was probably a case of complete transmission of infection.
Second, larger metropolitan population centers have the lowest total infection rate if the disease simply burns through the population. This intuitive paradox is understood when we think of the disease with a time course. In this sense, it has a passing similarity to the problem of a bank or investment group starting out finding places to invest money. There is a temporal limit to the transactions.
COVID-19 appears to have a 2–3 week course which is quite long. It appears to be infectious for up to 5–7 days prior to symptoms, if significant symptoms even appear. If you try out the software [3] and play with the incubation period, etc, you will be able to see how the graphs develop.
HLA (human leukocyte antigen) types and other genetic differences that regulate susceptibility to the illness in the first place, as well as ability to recover are not modeled in Epiflex. And yet, with most diseases these are present. With SARS there were HLA types that did not get the disease while others around them did [4].
Native Americans are historically far more likely to die of diseases like this coronavirus. This is why North America has very few left, and virtually zero without some european HLA genes. If Native Americans had the resistance of Asians or Africans, North America today would not likely be dominated by Europeans.
As one goes south in the Americas, the environment has been less friendly to transmission of enveloped viruses, so there are far more Native Americans with these susceptible genotypes.
We have epidemics at such long intervals (a generation time) that I think that a problem is that institutional knowledge tends to get lost. And R0 is taught, so that’s what gets repeated. R0 is derived out of epidemic results, it is not actually a “thing” out there in the real world.
References
1. Lloyd-Smith J, Schreiber SJ, Kopp PE, Getz WM (2005) Superspreading and the effect of individual variation on disease emergence. Nature. Nov 17;438(7066):355–9. https://www.ncbi.nlm.nih.gov/pubmed/16292310
2. Hanley B (2006) An object simulation model for modeling hypothetical disease epidemics — EpiFlex. Theor Biol Med Model. Aug 23;3:32. https://www.ncbi.nlm.nih.gov/pubmed/16928271
3. Electronic Data (Model package. .zip file) https://tbiomed.biomedcentral.com/articles/10.1186/1742-4682-3-32#Sec60
4. “Hong Kong researchers found that individuals with HLA-B*7303 gene type have much higher risk of getting Severe Acute Respiratory Syndrome (SARS) while those with HLA-DRB1*0131 gene type have much lower risk than the general population.” (The link is from the English version of China Daily in 2006. It isn’t live to the article anymore.)
