Non-pharmaceutical interventions (NPIs) such as lockdowns, social distancing restrictions, and mandatory face masks remain some of the most disliked responses to the pandemic. While many acknowledge their necessity, the toll that these measures have taken on businesses, livelihoods, and mental health has been exhausting for many.
These strict restrictions have also given rise to a vast array of new conspiracy theories, some of which have decried these NPIs as an attempt to remove rights. In a recent study published on the preprint server medRxiv*, researchers from the University of Vermont explore strategies for managing pandemics as well as model potentially optimal solutions.
Study: Should we Mitigate or Suppress the next Pandemic? Time-Horizons and Costs shape optimal Social Distancing Strategies. Image Credit: Khakimullin Aleksandr / Shutterstock.com
About the study
The researchers used a variational analysis approach that allowed them to derive functions that minimize or maximize a quantity over an interval in order to combine susceptible-infected-recovered (SIR) epidemic models that describe disease transmission with a function for both infection and social distancing costs over time. SIR models can determine future evolution quite accurately, as long as the parameters that enter the model do not change.
Unfortunately, with early pandemic responses fragmented and oft-changing, many early SIR models did not accurately reflect reality. However, using variational principles, model parameters can change to reach a pre-specified end state and time by selecting a trajectory that minimizes infection and social distancing costs, thus changing the SIR model to a fixed time horizon model.
The state variables typically used in SIR models are population densities of susceptible, infected, and recovered populations, with a constant disease progression rate from infected to recovered and a per capita disease transmission rates. The transmission rate divided by the per capita progression rate from infected to recovered reveals the R0, otherwise known as the basic reproduction number.
In this model, the transmission rate and reproduction number change over time, thus representing changes in social distancing policies and behaviors. This new number is the RD, and the Rt is the effective reproduction number that considers both the removal of susceptible individuals and changes in social distancing.
A third parameter, c, describes costs of social distancing compared to infection, and the last parameter, Tfinal, describes the time at which the pandemic as predicted to end. Other important values are S∞, which is defined as the proportion of individuals who would remain susceptible following the end of the pandemic, and sH, which is the maximum proportion of individuals who could be susceptible in a population that has achieved herd immunity.
The researchers divided strategies for dealing with the pandemic into two basic archetypes: suppression and mitigation. In a mitigating strategy, infection peaks before subsiding, and a substantial portion of the population becomes infected. This strategy aims to reduce the cost of social distancing.
Comparatively, the suppression strategy aims to prevent as many cases as possible, with a lower final proportion of infected individuals but enough recovered individuals to provide herd immunity. Optimal suppression strategies will not hold Rt lower than 1 indefinitely and optimal mitigation strategies will not allow completely uncontrolled pandemics.
One of the most important findings was that the perceived time-horizon and costs of social distancing can quickly lead to a switch from suppression to a mitigation strategy. In general, the higher the cost of social distancing and the longer the disease continues, the higher the chance that society will prioritize a mitigation strategy, and this switch can occur very rapidly.
Any pandemic close to the border of the mitigation/suppression threshold will likely provoke argument and disagreement. The researchers point out that their strategies took place in an idealized setting, in which there were no rapid changes in strategy or flip-flopping on policies.
The authors offer the tongue-in-cheek suggestion that these may have been better solutions than what they have proposed before suggesting that the strategies proposed have not been tried. They also identified poor communication and misinformation as some of the key reasons society fails to deliver these strategies, as well as uncertainty, complexity, and heterogeneity as pitfalls that could prevent society from delivering them in the future.
The methods explored here could help inform NPIs such as social distancing, mandatory face mask-wearing, and the closing of public places, both for the remainder of this pandemic and for the future. While the ‘mitigation strategy’ may seem callous to some, loss of livelihoods could lead to as many deaths as a disease in certain scenarios, and the mathematics explored here could help ensure the best possible interventions remain in place. Discomforting as this decision must be, hopefully, this research can help inform public health policymakers in the future.
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