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    Review of 'An Engineering Model of the COVID-19 Trajectory to Predict Success of Isolation Initiatives'

    An Engineering Model of the COVID-19 Trajectory to Predict Success of Isolation InitiativesCrossref
    Simple model describing the impacts of lockdown activities to the spreading of Covid-19.
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    An Engineering Model of the COVID-19 Trajectory to Predict Success of Isolation Initiatives

    Much media and societal attention is today focused on how to best control the spread of Covid-19. Every day brings us new data, and policymakers are implementing different strategies in different countries to manage the impact of Covid-19. To respond to the first wave of infection, several countries, including the UK, opted for isolation/lockdown initiatives, with different degrees of rigour. Data showed that these initiatives have yield the expected results in terms of containing the rapid trajectory of the virus. When this manuscript was first prepared, the affected societies were wondering when the isolation/lockdown initiatives should be lifted. While detailed epidemiologic, economic as well as social studies would be required to answer this question completely, we employ here a simple engineering model. Albeit simple, the model is capable of reproducing the main features of the data reported in the literature concerning the Covid-19 trajectory in different countries, including the increase in cases in countries following the initially successful isolation/lockdown initiatives. Keeping in mind the simplicity of the model, we attempt to draw some conclusions, which seem to suggest that a decrease in the number of infected individuals after the initiation of isolation/lockdown initiatives does not necessarily guarantee that the virus trajectory is under control. Within the limit of this model, it would appear that rigid isolation/lockdown initiatives for the medium term would lead to achieving the desired control over the spread of the virus. This observation seems consistent with the past summer months, during which the Covid-19 trajectory seemed to be almost under control across most European countries. However, recent data show that the virus trajectory is again on the rise. The latter is also consistent with the simple model proposed here. Because the optimal solution will achieve control over the spread of the virus while minimising negative societal impacts due to isolation/lockdown, which include but are not limited to economic and mental health aspects, the engineering model presented here is not sufficient to provide the desired answer. However, the model seems to suggest that to keep the Covid-19 trajectory under control, a series of short-to-medium term isolation measures should be put in place until one or more of the following scenarios is achieved: a cure has been developed and has become accessible to the population at large; a vaccine has been developed, tested, and distributed to large portions of the population; a sufficiently large portion of the population has developed resistance to the Covid-19 virus; or the virus itself has become less aggressive. It is somewhat remarkable that an engineering model, despite all its approximations, provides suggestions consistent with advanced epidemiologic models developed by several experts in the field.

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      Earth & Environmental sciences,Engineering
      Engineering model,The Environment,Covid-19,Recommendations

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      General assessment:

      This paper considers a topical and important subject, modelling the spreading of Covid-19, and especially using this model in predicting the efficiency of isolation/lockdown activities to stop the virus or at least to control its spreading, and protect the most vulnerable part of the population. These activities are based on the fact, that by decreasing the contacts between the individuals, we can decrease the spreading of the virus. Depending on the extent of these activities, their impacts on the society vary, but they inevitably have negative economic and societal effects. The legal aspects must also be kept in mind; the lockdown activities limit people’s rights of moving and communicating freely. This is clearly visible in the governmental actions in some countries. Now it seems that there are problems in getting vaccines to a wider use, and the virus itself shows no weakening, on the contrary, mutations that are more dangerous are developing, so we will be living in this world of temporary isolation activities for some time.

      This paper concludes that a series of strong but short- to - medium term activities are the best way to fight the virus. Timing of these activities is of primary importance: the time to start the measures, and may be even more important, when to lift them. The pressure to officials in both cases is remarkable, and this kind of model could produce more information to support the decision-making. The authors mention in Abstract that the summer 2020 is a good example of the power of isolation activities. The spread of the virus dampened considerably in the countries that took the maximal possible limitations into use. How much of this positive development is due to isolation activities and how much to the “natural” behaviour of the virus is unknown. Similarly, is the negative development towards the autumn 2020 due to too early lifting of the isolation or the virus itself? When more data will be available, the further research will shed more light on this.

      As a whole, this paper is a good example of using simple tools to solve complicated problems. As the authors say, it does not solve the whole problem, but to my mind, it could be one tool for decision-makers when planning new measures to fight the virus. The decision on using isolation measures is, of course, political and several aspects should be taken into account, but if the science can provide some impartial facts showing the consequences of the decisions, we can expect better results.

      The model:

      The model is a simple one consisting of two first order nonlinear differential equations with two variables (the number of uninfected individuals and the number of infected individuals). The model has two parameters (the infection growth rate constant and the constant for recovery/mortality), and it assumes the constant initial value for the population. The infection growth constant was modified so that it could take into account the isolation/lockdown activities. The model includes also an algebraic equation that calculates the number of individuals that are unable to pass on the virus because of the recovery or death of the individual in question. The model is a SIR (Susceptible, Infectious, or Recovered)-type compartmental model used for a long time in describing the propagation of infections in populations. The authors have extended the model so that the isolation/lockdown measures can be simulated.

      This is a very simple model and its advantages are the low number of parameters to be tuned and the ease of understanding its operation in spite of its nonlinearity. This kind of model has some weaknesses that must be remembered when applying it. It divides the population in three groups, and cannot handle e.g. age groups or groups with some basic illness separately. As a compartmental model, it assumes both compartments perfectly mixed. This problem could be solved by adding more compartments in the model, but with the cost of more differential equations and parameters. This, of course, would need more detailed data, too. The model is deterministic and many phenomena concerning with the propagation of the disease are stochastic. The model also describes the recovery/mortality with one constant, only. Releasing this assumption means that we have to divide the third compartment in two (SIRD model). In the proposed model, the recovery provides the individual with the immunity. We do not have information enough to know, if this immunity is only temporary. These are the questions needing further research.

      The model has been tested using the data from China, South Korea, and Singapore; all highly and densely populated regions. This raises the question of the requirements for the region to be modelled. Is there any minimum number of the initial population Po, or the population density? How does the model work in Europe at the country level, or should we group the countries according to some criteria (economic area, social behaviour, Covid-19 strategy), and model larger regions? The results for UK seem encouraging as for the model performance, but we are still dealing with a densely populated region. The lockdown has in some cases focused on the traffic between countries, and in some cases, it means a severe discontinuity in the working traffic during both the start and stop of the lockdown. A good example is the situation in Finnish and Swedish Lapland, especially in today’s situation when the strategies for fighting the virus are so different in each country. The situation is very much the same in countries that live on tourism. This fits also with the Finnish Lapland where the first case, exactly one year ago, was a tourist. Is there any need to take into account these kind of “exogenous” infection sources?

      Another question that the authors might comment with few words is changes in the virus. How does it affect the two constants, if the virus is mutating to the direction of higher transferability (as it happens now) or of higher mortality? Can the model cope with it? What, if we had a mixture of mutated viruses with different properties?


      The model was validated with the WHO data for China, South Korea and Singapore. These countries were chosen because of three reasons: long-time data was available because of the early encounter with the disease (the first study was carried out already in April 2020), high cohort numbers, and cultural similarity. The results together with testing the model with more recent UK data show that the model with a proper parameterisation gives a good fit with the recorded data. There is one exception in the China case, but it seems to be due to problems in data acquisition. Delays in feeding the test results e.g. during the weekend seem to be quite common, and it puts some stress on data pre-processing.


      Section 6 summarises well the results and findings of the study. Adding few lines on the limitations of the model and further research/development directions will answer my earlier comments and questions.

      Some corrections:

      There are two Sections numbered as Section 4. The easiest way to correct this is to put these Sections together. The authors should also check the caption of Figure 3. Just before Section 6, there is a reference to Figure 2B. Figure 2 has two panels, but they are not numbered, so the reference should be “the right panel of Figure 2”. On the first line of Section 6 there is one “time” too much. There are also some minor typos in the text.

      Oulu, Finland, January 31, 2021

      Kauko Leiviskä


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