Modifying SEIR models to explore the role of average household size in the era of lockdowns and social distancing

Compartmental models have long been used to study the dynamics of infectious diseases without requiring the intensive computational power of more detailed simulations. The well mixing assumption on which they are based is typically valid when people are meeting a significant number of other people each day. However, in the Covid-19 era of lockdowns and social distancing, the number of non-household contacts has dropped significantly. Standard SEIR models cannot produce the expected result of an idealised lockdown (i.e. no non-household contacts), where the final number of infected is less than the average household size times the number of infected and exposed at the time of the lockdown. To correct this anomaly, we separate the household and non-household contributions to the total cases and apply a carrying capacity to the household acquired cases. Finally, we illustrate the application of the model to two countries with completely different approaches to managing the SARS-CoV-2 pandemic, New Zealand and Sweden. The sharp drop in cases in New Zealand following their lockdown can be well explained with a carrying capacity model, while we show that the Swedish approach could be extremely risky for countries with higher average household sizes.
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