You may recall the important paper suggesting that due to variation in susceptibility to infection, population immunity might be reached at far lower levels than traditional formulas would suggest. An independent statistician has used the ideas presented in the paper to build a model which confirms that population immunity could be achieved at these levels. (Lewis Analysis) Mr. Lewis takes as his starting point the Imperial College model, which found that population immunity would not be achieved til around 50% to 60% of the population had been infected, and that 81% of the population overall would be infected. However, that model assumed all individuals were equally susceptible and equally infectious, with the exception of variation for household size and geographic separation. The author then builds a traditional SEIR model, but adds greater variation in both susceptibility and infectability. In his unadjusted model, population immunity begins to kick in around 58% of people infected. When he added assumptions of greater variation, population immunity begins at around 25% of the population infected in one model and around 7% in a model with greater variation. These results do suggest that, variation in susceptibility and infectability, if they exist, have an enormous impact on the achievement of population immunity.
And here is another paper on population immunity. (Medrxiv Paper) In this one the authors also diverge to build a model with greater variation in susceptibility. They do this by adjusting the contact model by age bands and by activity levels, and c0-vary those two factors in modeling how an epidemic might proceed and when population immunity might be achieved. Models with greater variation in age group contacts and activity levels have much lower population immunity achievement levels. Variation in activity level plays a greater role than age group variation. They include models of mitigation of spread measures. The strictest measures provoke the strongest second waves. Other measures have basically no follow-on wave. They note that including even more factors relating to variation in spread would potentially lower the threshhold for population immunity further.
Another paper cites the role that population density may play in the rate of spread of infections. (Density Paper) The authors use data showing greater connectivity and contacts among individuals as cities grow in size. This would clearly factor into estimates of infection spread speed and extent.
This paper discusses the role of heterogeneity in infection spread. (Medrxiv Paper) A group of researchers from China examined a small outbreak in a Chinese city and attempted to track the trains of transmission. They found strong variation across transmission chains, with at least one individual being a “super-spreader”. This finding of heterogeneity in transmission undermines models that assume equal likelihood of susceptibility and infectivity.