When a new infectious disease appears, the lack of an effective treatment or vaccine strategy often results in the application of non-pharmacological interventions (NPIs) or containment measures, including testing for infection, tracing contacts, and isolating potential sources of infection.
A new study published on the preprint server medRxiv* in May 2020 discusses the benefits of staggered re-openings in each locality based on a global set of parameters that determine the suitability of containment measures or otherwise.
The decision to impose a lockdown on a vast region is fraught with tension since it imposes constraints on physical movements to the extent that regular business and other economically productive activity is curtailed, as well as school closures, which throws the normal balance of modern social life out of kilter.
Why Stochastic Models?
In many cases, the data collected on cases over time is most naturally analyzed by compartmental models that are based on the assumption of a population that is homogeneous in its composition. An epidemic curve can, however, also be less clear on the relationship between the spatial and temporal distribution of the illness.
This is because infections often cross the boundary between neighboring populations. Early outbreaks are characterized by a low number of cases and, therefore, unpredictable or stochastic effects. Later, both randomly distributed cases and those traceable to travel-based connections are found.
This is different from the middle stage of the outbreak, with a high number of cases. At the later stages, therefore, if travel restrictions are removed all at once, cases may increase drastically in number.
Local Trigger-Based Reopening Strategy
The researchers from the University of Guelph and the University of Waterloo suggest that "a phased approach to open or close schools and workplaces, based on 'trigger' conditions such as the number of local confirmed positive cases, might be better." The phasing could operate on a temporal or spatial level.
In the former, the phasing relates to the timeline of the re-opening of social gathering places, including workplaces. Some might be suitable for earlier re-opening than others.
Another type of phasing refers to the area-wise distribution of cases. Smaller towns or localities would, in this case, be opened first, based on the theory that the force of infection is markedly lower in a small population because of stochastic fade-out, compared to larger populations. Other factors contributing to this include the lower rates of inter-individual contacts and less travel, which means that fewer infections are imported.
The Questions to be Answered
The current study is aimed at developing a stochastic model of virus transmission as well as testing and lockdown measures, based on spatially-phased re-opening of regions, that will provide answers to three important questions:
- Is county-specific or province-wide relaxation of school and workplace closure to be preferred?
- Is it worthwhile to coordinate testing programs and criteria to be fulfilled for re-opening counties?
- What is the limit of the performance of a spatially-phased re-opening strategy in an early outbreak?
The results may help schedule a roster as well as the timeline for the re-opening schools and workplaces with the fewest possible number of infections and person-days lost because of lockdowns, both in the early and late stages of the epidemic.
What Model was Used
This computational model is called an ABM or agent-based model. It deals with a population that is scattered across several centers termed counties. The spread within each county follows the SEAIR model - S is susceptible to infection, E is infected, but not yet infectious ('exposed'), A is infectious but asymptomatic ('asymptomatic'), I is both infectious and symptomatic ('symptomatic'), and R is recovered (are isolated and no longer infectious).
The researchers assume that symptomatic are diagnosed each day with some certainty, while the spread outside schools and workplaces is limited by physical distancing. A second assumption is that physical distancing increases with the number of cases.
They simulated re-openings over a period of one year to find the projected number of cases, beginning with a 50-day period of closure that begins every time 50 cases are accumulated. The next step diverged into two routes: each county is locked down or closed separately according to as a certain number of cases is reached (the 'trigger' prevalence), or the whole province is re-opened or re-closed globally each time the trigger prevalence is reached.
The model thus shows changes in lockdown measures based on two types of regimes – one in which COVID-19 remains at an endemic level throughout the simulation, which occurs in counties with a high population density, and sporadic cases with intercounty spread through travel, in sparsely populated counties.
The Results of the Model
While either strategy shows the same pattern of infection, the types of closure and the area affected show gross variation. With the global strategy, most of the counties are shut down most of the time.
The local re-opening strategy appears to do far better at most trigger prevalence values. If this trigger value is very high, such as 1,000 cases/100,000 population, the spread occurring at work and in schools will likely cause infection of much of the population. If the trigger prevalence is low, on the other hand, sustained lockdown leads to very low infection levels for most of the year by either route.
The aim is to find the trigger prevalence for the local re-opening strategy where most of the province remains open for most of the year, for the smallest possible increase in cases. The ability to achieve this is due to the flexibility this strategy gives to close down only areas where outbreaks are active (probably the more densely populated counties).
The optimal trigger prevalence will be that which allows the number of person-days lost because of the lockdown, yet allows only a 1% increase in cases above the minimal value of the trigger.
The Essential Nature of Coordination
This strategy has a limitation: different counties can adopt different triggers, which could impair the success of the strategy. In such a situation, more person-days will be lost to closure than to the rise in infections. The reason is that infections are transmitted between counties due to a too early relaxation of lockdown measures.
This, in turn, will trigger lockdowns in these counties, which further increases the number of person-days in closure. In short, this route can be successfully adopted only if there is proper coordination across counties.
The same principle applies to testing in different counties. The model shows that as the rate of testing for individuals with infection shows increasing variations between counties, the percentage of people infected, as well as the number of person-days lost to closure, will also go up.
The Phenomenon of Policy Resistance
Many populations have expressed dissent at lockdown measures, which is linked to s social phenomenon termed policy resistance. This means that the success of some interventions is partly reduced because of nonlinear behavioral feedback. This is quite typical of all interactions between humans and natural systems.
The behavioral response to the current pandemic has shown itself in two opposing forms, namely, increased physical distancing with a higher number of cases, vs. increasing resistance to lockdown.
Here again, a local re-opening strategy based on good quality evidence could meet with better compliance from populations who resist lockdown over a whole province but may accept it over a localized part. Secondly, local authorities may be able to close down more quickly compared to the more lengthy process at the provincial level.
Limitations and Future Directions
The model discussed here has some limitations. For one, it assumes that county authorities will close down as soon as the trigger prevalence is reached. Delays will allow more cases and, in a few weeks, more deaths. In addition, the trigger prevalence is only optimal if it is used to close down the county at that point.
Including ICU capacity and the population's age composition could improve the model's reliability and help to project the results of even more localized closures, such as only high schools and colleges, while leaving elementary and primary schools open. Again, once a certain percentage of ICU beds are occupied, the county could be closed down. The importation of cases from outside the province could also be included since this will be a valuable source of infection once local control is reached.
The model shows the critical role of stochastic models based on the spatial case and population distributions, to derive the best strategy to exit lockdowns at local vs. global levels.
*Important Notice
medRxiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.
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