Cluster epidemic makes this outbreak more dangerous
There are several patterns for the spread of infectious disease. Commonly an infection will just spread from one person to another randomly.
However, the spread of Covid-19 represents a cluster epidemic, which is one of the more unusual patterns of spread. This spread is from one group of people to another group of people. Once in a group, their closeness of contact, time spent together, and what they are doing, allows the infection to spread most easily among the group until the infection runs its course and dies out within that group.
Family groups often provide the easiest transmission. The infection, including the Delta variant, has much more difficulty getting from one group of susceptible people to another, but this can occasionally happen from one of the many transient encounters occurring in a socially mixing population.
Therefore, there are two important transmission rates. First, there is the usual person-to-person transmission rate within a group. Second, and most importantly, is the transmission rate from one social group to another. The second transmission rate and the size of the infected networks drives the number of cases that occur.
Therefore, it is the frequency of the occurrence of new sub-clusters relative to the frequency with which sub-clusters are contained or resolved that determines the control of the spread of infection.
The size of a group containing infected members can also make them difficult to completely isolate, and can also produce ongoing cases within the contained group for many weeks. The overall reduction in the number of people infected is determined by the combination of the number and average size of the sub-clusters being prevented and, therefore, the number of new cases can decrease very quickly.
The features of cluster-based infections make them controllable by changes to the way people interact. These methods of control are not effective against many other infections, such as measles, that are so infectious they do not stay in groups of people for very long and spread widely before symptoms occur.
The infection of Covid is greatly weakened by limiting contact between social groups through lockdowns, the rapid identification of contacts, and the isolation of all members of infected groups before any member has spread the infection to another group. Isolation of people and their contacts can also occur if they are being sought by the police.
At the beginning of the latest level 4 lockdown in Auckland there were seven sub-clusters generating the cases reported. The level 4 lockdown produced a reduction to 8-10 new cases a day.
Since easing to level 3, the number of new cases hovered around 50 a day for over a week, with about the same number of sub-clusters. This effect on case numbers suggests that level 4 was about five times more effective in combating infection than level 3.
The minimal change in the number of sub-clusters indicates that the sub-cluster replacement ratio is currently about 1. That is, for every sub-cluster contained or resolved each week, a new subcluster has formed. This dangerous situation has persisted, and now two large sub-clusters are making significant demands on the contact tracing and isolation workforce.
A sub-cluster replacement ratio of 1 also indicates that we may still be able to control this outbreak. The next six weeks will be crucial.
From what has happened in Melbourne, Singapore, and the UK, about 8000 cases of Covid and numerous deaths in Auckland have likely been prevented by the contact tracing and isolation workforce over the past two months. This ongoing contact tracing workforce, although it might be seen as expensive, is vital for the control of the infection.
Vaccination reduces the frequency of sub-clusters of infection, but the size of outbreaks is less able to be controlled by it. That is because the proportion of people vaccinated within each group is likely to vary considerably and, once infection is introduced, it tends to run its course until it finds no new susceptible people in the isolated group and dies out.
Therefore, the effectiveness of vaccination may be determined by the groups with the lowest rates of vaccination and not the overall national average vaccination rate. Vaccination may greatly reduce the transmission rate between groups, and produce a rapid reduction in the cases, but this is likely to be influenced by the size of social groups and the rate at which they mix.
Therefore, vaccination of the young, especially those in the interactive educational environment, will be an important step in the control of the infection.