A simple model of CoV2 transmission

I created this simple model to clarify – in my own mind –the selective pressures on viruses such as CoV-2 that we can expect in various settings. I’m considering three strains: firstly, an “ancestral” strain with an intermediate growth rate and a moderate incubation period; secondly, a very aggressive mutant that has a short incubation period and causes the human host to emit (“shed”) a lot of virus particles very quickly; and, thirdly, a mild mutant that has a long incubation period and causes only minor symptoms.

My conclusions are:

  1. In institutions such as boarding schools, care homes, and hospitals, the aggressive strain (red) has a competitive advantage. We can expect that strains that are transmitted within institutions will increase in virulence. We should therefore isolate patients from each other as much as possible, and be careful to prevent these strains of CoV-2 from escaping into the community by e.g. infecting doctors and nurses.
  2. In a normal community, and also in a community that is in “lock-down”, the mild strains (green) have a competitive advantage because they are shed for longer – as a result of their longer incubation periods. The probability of transmission of each is roughly proportional to the areas “under the curves”, colored below with solid blue, red and green.
  3. Over time we can expect mild strains to dominate – as they always have eventually in previous epidemics (especially after a significant number of individuals have acquired immunity).
  4. The competitive advantage of the mild strain is slightly increased by lock-down. This is because there is less chance that the sick individual infects more than one new host. If two or more hosts are infected, the more aggressive strains are favored because they release “daughter” virus particles earlier.

Here is my model:

Model of CoV-2 transmission 4.png

Description of the model.  At the top I’m showing how the illnesses caused by the three hypothetical strains might develop over time within their individual hosts.  The vertical axes show “shedding”, i.e. the amount of virus that the sick individual is continuously transmitting into his or her environment.  Once the sickness progresses enough to cause a fever (dotted line), I assume that the victim goes home and to bed, and no further infections take place.  (Of course they might in reality still transmit the illness to other members of their family, but for simplicity I will ignore this.)  In the three lower panels A, B and C, I’m showing the human contacts that have the potential to spread the virus.  Each dot represents an opportunity for infection to take place.  The top panel, (A), shows a community before lockdown measures are enacted, (B) shows a community once lockdown is in place, while (C) shows an institution such as a care home or hospital where several accidental contacts take place each day no matter how sick the patient becomes.  I have also shown that the blue and green strains are outcompeted by the red – bear in mind that strains can compete with each other within each patient.  The times of the contacts (dots) were defined by a random number generator, with 2 to 3 contacts per day in the normal community (A), only one contact every few days in lockdown (B) and about four contacts per day in the institution (C).

Please note that these trends are driven by differences in incubation periods (or, to be precise, differences in {incubation periods – latent periods}), not by the deaths of hosts in the case of the virulent strain – which happens too late.

______________________________________

The Hypothesis

For a general discussion of the seasonality of respiratory viruses, written for the layperson, please see

Every winter, colds and flu increase

For detailed scientific information about the seasonality of respiratory viruses, including discussion of the trade-off model, viral dormancy and much else, see my 2016 paper:

Shaw Stewart, PD.  Seasonality and selective trends in viral acute respiratory tract infections. Medical Hypotheses 2016; 86 104–119.

For a discussion of the strange timing and duration of influenza epidemics, please see

The strange arrivals – and departures – of influenza epidemics in the UK, 1946-1974

Applications to Covid-19

For information about the probable seasonality of Covid-19, and whether we can expect it to become rarer in the summer, or reappear in the fall, please see

Predicting the seasonality of Covid-19

For comments about the epidemiology of Covid and other respiratory illnesses, please see

Epidemiology of respiratory illness

For discussion of how the trade-off model can be applied to the Covid epidemic see

Covid 19 and the trade-off model

For a simple model of the transmission of viruses such as CoV-2, please see

A simple model of CoV-2 transmission

For comments about how quickly we can expect viruses to adapt to new environments, please see

Adaptability or respiratory viruses

For more detailed scientific points about CoV-2, see

Technical notes on CoV-2 for scientists

For practical tips on avoiding respiratory illness see

Suggestions for avoiding colds and flu – and Covid-19

 

Model of CoV-2 transmission 4.png

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