In a typical pandemic a virus spreads easily between individuals of all age groups, sweeping through a population. However, SARS-COV-2, which causes Covid-19, spreads differently. It does not appear to spread easily between young children and usually requires relatively prolonged close contact to spread between adults and from adults to children.
The requirement for such ‘contact networks’, from within which clusters of cases arise, is typical of a cluster epidemic.
This fundamental difference between normal pandemic spread and a cluster epidemic influences the course of the epidemic, the methods needed to model it, and the actions needed for its control. Control of a cluster epidemic requires a primary focus on reducing transmission of the virus between ‘contact networks’ of people, not so much on reducing transmission between individuals across the population.
Understanding this can help explain New Zealand’s epidemic, and control was achieved more rapidly than predicted by standard pandemic models. We can consider a population not as individuals but as a number of, potentially overlapping, contact networks – groups of individuals who interact more intensely, for example, families, work colleagues, arts groups, or sports clubs.
The population would then be represented as N contact networks. When a virus produces a cluster of cases, it infects a contact network which has features promoting its spread, and a significant proportion of members can become infected. The cluster of infective cases reduces to zero when the virus has died out within the network, as long as there are no further virus incursions from outside. An infected person in the network can ‘set off’ another cluster by participating in another contact network which promotes transmission. Therefore, a defined cluster may involve several contact networks.
A cluster epidemic can be approximated by a simple compartmental model, with contact networks rather than individuals, as the primary focus (unit of interest). The most important measures then become the average network-to-network transmission rate and the average recovery rate of infected contact networks.
The ratio of the average network-to-network transmission rate to the average recovery rate of infected contact networks (R-network) can be calculated, and represents the average number of new infected contact networks produced from an infected contact network.
When R-network is less than one, fewer new infected contact networks occur than are being resolved and control is being achieved. The network-to-network transmission rate for Covid-19 may be as low as 0.7 percent, which, although low, would still produce another infected network for each 143 networks infected. However, the network-to-network transmission rate would be much greater if many contacts are untraced or quarantined too late.
A cluster epidemic can advance rapidly. The increase in cases occurs spasmodically but quickly rises as successful transmission from one contact network to another, even through only one person, leads to a cluster of multiple cases each time.
However, this is also a major advantage for cluster epidemic control. As the transmission rate from network-to-network is reduced through quarantining contacts, the number of people infected also reduces rapidly. This is because whole clusters of cases are prevented. In New Zealand, a rigorous lockdown prevented contact network-to-contact network transmission.
Infected networks were contained by effective quarantine of their membership, so broad elimination was achieved quickly. Elimination occurred at a pace in keeping with the average size of clusters prevented, reducing the number of active cases markedly in a relatively short time. A high quality rapid case isolation and contact quarantine management system could achieve the same outcome, especially in the context of other general measures to limit circumstances that promote virus transmission.
Countries that have not achieved containment of the epidemic during lockdown have not managed to rapidly identify sufficient numbers of the contact networks of cases and quarantine their membership. Thus, while some reduction in the incidence is achieved due to lockdown, network transmission commences again when lockdown ends.
However, control is still attainable. Cases will still tend to occur predominantly within contact networks, albeit in a complex distribution. Also, control measures do not need to be perfect. If rapid identification and quarantine of over 80 percent of members of an infected contact network occurs within the average incubation period, the risk of that network transmitting the virus to another network is dramatically reduced and the epidemic is likely to dissipate
The approach to the control of a cluster epidemic and prevention of its recrudescence should focus specifically on the types of contact network that promote transmission of the virus that is causing it, and the measures that are required to stop its spread from one contact network to another.
At a population level, aged care facilities and certain types of gathering should be a focus, and when gatherings do occur, specific public health measures should be encouraged, such as social distancing where possible, cleaning of commonly handled areas, and the availability of hand sanitiser and masks. Individuals will need to develop a new normal of behaviour in relation to personal hygiene. They should be informed about the types of contact networks that promote SARS-COV-2 transmission and how to avoid transitioning frequently between such networks. Since households themselves represent high transmission contact networks, this will be an ongoing challenge.
The reason New Zealand eliminated Covid-19 earlier than expected is likely due to the nature of Covid-19 epidemics. SARS-COV-2 causes cluster epidemics. Rapid control was achieved because blocking individual transmission events between contact networks prevented further clusters of new cases from developing.
