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Mathematical modelling of intervention timings by Prof Istvan Kiss and colleagues

• Sussex mathematicians looked at one-shot short-term measures
• The optimal timing of an intervention to reduce the maximum demand on healthcare could result in two peaks
• The optimal timing of an intervention to reduce the overall number of infected people may lead to one single larger peak

As COVID-19 spreads across the UK and around the world, many people are asking when is the right moment for governments to make major interventions to slow the spread of the outbreak. 

Professor Istvan Kiss is a Professor of Applied Mathematics at the ÅÝܽ¶ÌÊÓƵ and is an expert in modelling how diseases spread.  He, together with Dr Joel C Miller (La Trobe University, Australia) and Francesco Di Lauro, a research student from ÅÝܽ¶ÌÊÓƵ, have  which looks at the question: if policy makers have a one-shot major intervention to make, when should they make it?

This new mathematical modelling finds that if the objective is to safeguard the ability of health services to cope, policy makers should intervene early and aim for two small peaks in infections, rather than one large peak. However, an intervention with the aim of reducing the overall number of infected people may lead to one single large peak.

The analysis found that:

• if the control measure can only be implemented for a short time, it is best to delay its use until a time when it will directly block as many transmissions as possible;
• if an intervention is sustainable, it should be implemented early and maintained until the epidemic is under control.

School closures could be considered either a long or short-term measure, where short-term means a couple of weeks and long-term means several months. That's a decision for policy makers. 

The paper also found that if the aim is to reduce the height of the peak (the number of people infected at the outbreak’s most intense moment) then the intervention should be started earlier. This results in two lower peaks, as people return to their normal behavioural patterns when the intervention has been stopped – or when they have grown tired of it - and then the infection may begin to spread again.  In this second scenario, it is likely that more people will be infected overall but the impact on the health service is spread out in time. 

Professor Istvan Kiss from the School of Mathematical and Physical Sciences at the ÅÝܽ¶ÌÊÓƵ, says:

“To be clear, our analysis only considers measures that are not sustainable in the long run. Of course, if an intervention is sustainable (such as social distancing) then this should be implemented early and maintained until the outbreak is bought under control. Our analysis shows that a one-shot short-term intervention is more effective if it is implemented when it will directly block as many transmissions as possible – although the exact moment that you implement a major one-shot intervention depends on what you’re trying to achieve. If sustainable control measures are not enough to stop an epidemic then more drastic measures can be considered. If these are brought in too early it is likely that the outbreak will result in two or double peaks, with potentially more people infected overall but the demands on the health service being more manageable. Of course, we as mathematical modellers are not in a position to decide which measures are sustainable and which are not.

“Individuals already seem to be opting to practice “social distancing” – such as avoided densely populated events – and for many this is a sensible idea.  The effect of such social distancing is that the peak of the epidemic is both delayed and less people will become infected.

“We’re in a different situation than we were in with the H1N1 pandemic in 2009.  The fatality rate for COVID-19 is higher and that means that what might have constituted a one-shot drastic intervention for H1N1 might be considered to be more tolerable for a longer period now.”

Francesco Di Lauro, a PhD student and doctoral tutor in the School of Mathematical and Physical Sciences at the ÅÝܽ¶ÌÊÓƵ, said:

“Our models address the biggest question facing the world right now: what should governments be doing in response to the COVID-19 pandemic? If governments want to make a drastic intervention, they probably only have one chance. This is the most critical public heath decision facing governments in a generation – they’ve got to get it right.

“As a PhD student it’s been absolutely fascinating to work on this important paper – we’ve been working around the clock on the analysis. We plan to publish more soon, and we’re reviewing our results as we watch the evolving situation and the emerging data.”

Dr Joel C. Miller, a Senior Lecture at the Department of Mathematics and Statistics at La Trobe University in Bundoora, Australia, said: 

“In the face of the current pandemic, it is important for governments to be aggressive in their interventions and act quickly.  However, some interventions simply cannot be sustained for a long period.   These interventions have little overall impact if they are applied too early, but if they are timed right, they can have a significant impact on the course of the epidemic.”

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