Modelling the pandemic
BMJ 2020; 369 doi: https://doi.org/10.1136/bmj.m1567 (Published 21 April 2020) Cite this as: BMJ 2020;369:m1567Read our latest coverage of the coronavirus pandemic
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Dear Editor,
I was very interested in the BMJ Editorial 21st April, particularly the main title: Modelling the pandemic, a topic with multiple dimensions and potential output for tailoring intervention. I was also interested in the second rapid response letter noting different international “CoViD-19 life cycle curves”. Several reports reflect on geography and ethnicity as factors influencing the mortality and degree of prolonged morbidity from COVID19. A recent UK report was the 7th May UK Office of National Statistics brief online publication of comparative UK death-rates from COVID-19 (Syn. SARS-CoV-2), noting significant differences in mortality between different ethnic groups, after adjusting, by location, for socioeconomic and population density issues. Another report, currently in preprint (https://doi.org/10.1101/2020.05.06.20092999), presents a detailed analysis of COVID-19-related hospital deaths among adult NHS patients, finding ethnicity an important factor.
The differential international pattern of case-fatality and prolonged morbidity rates is clearly apparent in current academic online sites, derived from multiple online data sources (e.g. https://coronavirus.jhu.edu) and is consistent, on a global basis, with a genetic-susceptibility effect. Mainland Southeast Asia (MSEA), where most coronavirus species originate and exist, consistently shows much lower or even zero national case-fatality rates and much-less persistent morbidity rates from COVID-19 than elsewhere in the World. For instance, useful running summary histograms from one of those online sources most currently (10 May), show Singapore with 23,822 COVID-19 cases diagnosed since the index case on 23rd January 2020, but no deaths, and only 1097 cases still hospitalised (https://en.wikipedia.org/wiki/COVID-19_pandemic_Singapore). Comparisons with other nations, can be made by changing the nation in the link.
We all need an effective vaccine, but there has been concern widely expressed, that the first vaccines currently being trialled might not necessarily give solid immunity to all, perhaps because of some hypothetical lack of specificity in some of our immune systems. While the above regional and ethnic differences predict an even greater tragedy unfolding amongst some populations, particularly of African ancestry, they also offer some opportunity for a targeted, safe, engineered vaccine that could lend that putative innate MSEA COVID-19 protection to all of us irrespective of origin. Excitingly, preliminary evidence of that possibility and the practical components of its solution have already been offered in several published reports - see below.
It is proposed here that a COVID-protective genetic locus can be identified in the human Major Histocompatibility Complex (MHC) where our adaptive immunity engine resides. On statistical inference, there is a clear candidate locus, namely human leukocyte antigen allele group HLA-A*11, which is present at very high allele frequencies in most MSEA populations: ~0.30-0.58 [1] i.e. phenotypically detectable in ~50%-90% of individuals. However, HLA-A*11 is absent from all Sub-Saharan populations tested and in most individuals of recent African ancestry living elsewhere. It was postulated that HLA-A*11 was acquired from archaic Denisovans after the ancestors of modern Eurasians left Africa [1]. Amongst W. Eurasians Its allele frequency is ~0.05-0.1, with correspondingly low overall phenotypic frequencies, and ~0.07-0.2 allele frequencies are observed in S. Asians [1] Presumably HLA-A*11 was strongly selected for in survivors of local disease. (see also World map of allele frequencies: www.allelefrequencies.net/hla6008a.asp?hla_allele=A*11: )
Bats may be the main host of coronavirus sp. [2] as the multiple zoonotic coronavirus species recently found in a bat & bat-guano survey in central Myanmar imply: 6/7 coronavirus species identified were novel and local to Myanmar and all those are yet to be identified in a human host [2]. Whether MSEA is/was the main virus homeland is another matter.
In experimental support of specific HLA-A*11 enhanced protection, HLA-A*11:01 binds particularly well with a unique nucleocapsid protein peptide found in all SARS-CoV isolates [3][4], indicating potential for peptide-epitope engineered vaccine-development. This last is theoretically feasible; for instance, a direct practical experimental approach found that adjuvanted multi-epitope vaccines protected HLA-A*11:01 transgenic mice against another Worldwide zoonosis Toxoplasmosis [5].
Given the urgency, difficult questions include: How easy and speedy would it be to:
1) Engineer and experimentally test a hypothetical bespoke vaccine (or any other epitope-engineered vaccine for that matter) - and 2) then progress to ethical trial in humans – in parallel or after trials of more ‘off-the-shelf’ vaccines currently under approved trial?
Stephen Oppenheimer (FRCP retired.)
Green Templeton College, Oxford
[1] Abi-Rached L, Jobin, MJ, Kulkarni, S, (& 20 others). The Shaping of Modern Human Immune Systems by Multiregional Admixture with Archaic Humans. Science. 2011; 334 10.1126/science.1209202
(see also World map of allele frequencies: www.allelefrequencies.net/hla6008a.asp?hla_allele=A*11: Note- the same webpage www.allelefrequencies.net/ also has an large table of worldwide individual population frequencies accessible by searching for the same A*11allele).
[2] Valitutto M, Aung O, Tun KYN (& 15 others). Detection of novel coronaviruses in bats in Myanmar. PLoS ONE (2020) 15(4): e0230802. https://doi.org/10.1371/journal.pone.0230802
[3] Blicher T, Kastrup JS, Buus S & Gajhede M. High-resolution structure of HLA-A*1101 in complex with SARS nucleocapsid peptide. Acta Crystallographica Section D. (2005). D61, 1031–1040
[4] Prachar M, Justesen S, Steen-Jensen DB, Thorgrimsen S, Jurgons E, Winther O, and Bagger FO. COVID-19 Vaccine Candidates: Prediction and Validation of 174 SARS-CoV-2 Epitopes. bioRxiv preprint doi: https://doi.org/10.1101/2020.03.20.000794
[5] Bissati KE, Chentoufi AA, Krishack PA, Zhou Y, Woods S, (& 21 others). Adjuvanted multi-epitope vaccines protect HLA-A*11:01 transgenic mice against Toxoplasma gondii
JCI Insight. 2016;1(15):e85955. doi:10.1172/jci.insight.85955.
Competing interests: No competing interests
Competing interests: No competing interests
Dear Editor,
In this response, I take issue with the pessimistic view of Devi Sridhar and Maimuna Majumder [1] on axiomatic modeling in epidemiology and defend this way of informing nonpharmaceutical interventions. In "Modelling the pandemic," the authors claim that our current mitigation and suppression measures deployed to cope with the SARS-Cov-2 outbreak are guided by (and over-rely on) mathematical models. They highlight the reliance of mathematical models on certain assumptions and point out at the value-ladenness of decisions regarding the inclusion or exclusion of factors from such models. As a solution, the authors advise making both data and code publicly available to ensure replicability and supporting modeling with other types of evidence such as case studies of policies implemented in other countries, anecdotal evidence from frontline healthcare workers, and studies of previous epidemics.
Even though I lean towards the view that supporting decisions with different types of evidence is beneficial, I am concerned that we currently lack studies that assess the efficacy of nonpharmaceutical interventions other than the above mentioned models. The first study [1] employing natural experiment design to assess the response in China was published weeks after similar measures had to be introduced in other countries. Using evidence from previous outbreaks, while possibly informative, requires extrapolating results onto the current epidemic because each pathogen is characterized by specific features and infectiousness, leading to pandemics having different and sometimes unique characteristics. The data needed to identify a degree of similarity between SARS-CoV-2 and some previous outbreak is likely to be sufficient for establishing efficacy claims on its own (known in philosophical literature as the extrapolator's circle). Moreover, even though the first-hand experiences of healthcare professionals may be very informative concerning caring for Covid-19 patients (e.g., such as suggesting prone positioning [3]), they are unreliable in assessing nonpharmaceutical interventions targeting social behavior and those which are not in a healthcare environment.
Since this is the situation we find ourselves in, the mitigation responses have to be informed by axiomatic models. Moreover, the lack of empirical evidence is likely to constrain the quality of decisions regarding mitigation measures. Regrettably, even though epidemiologists have used compartmental models (such as SIR – susceptible, infectious, and recovered) for over a century, they have never been considered in the context of evidence-based medicine. None of the standard evidence hierarchies and assessment tools explicitly mention axiomatic models. The Oxford Centre for Evidence-Based Medicine [4] lists mechanism-based reasoning at the lowest stage, and NICE guidelines [5] do not include epidemiological models or mechanistic reasoning. This indicates the need to consider what type of evidence (if any) can be delivered by axiomatic models. Is this type of evidence as reliable as RCTs, or does its exclusion from the hierarchies of evidence stem from a lack of faith in their functioning?
A clarification is in order here. Sridhar and Majumder, despite exemplifying their discussion with an agent-based model, focus on mathematical models. While the SIR framework and its more advanced derivatives (which are the primary group of mathematical epidemiological models) have been used for predicting the development of the epidemic [6] [7], policy decisions have actually been led [8] by agent-based models (ABMs) [9] [10]. They differ from mathematical models in terms of both their advancement and use. First, ABMs cannot be solved mathematically and require the use of computational methods (e.g., simulation). Second, the most advanced ABMs currently simulate the society of agents exposed to the risk of infection during social interactions in different contexts (at household, work, community, etc.). The input to ABMs differs significantly from the axioms of standard compartmental models. The rules setting the behavior of agents are calibrated to statistical data describing work and commuting habits, travel distances, and neighborhood interactions, making the society of agents similar (in epidemiologically relevant aspects) to the societies represented with these models. The assumptions describing the infectiousness of the pathogen are also informed empirically. Often, calibration to the epidemiological data from the beginning of the outbreak is applied.
It remains true for ABMs that "[a]ll models are limited by the assumptions that they make," however, this alone is insufficient grounds for skepticism regarding this method, especially if no other evidence is present and decisions need to be made. All results in medicine rely on assumptions. In vitro and animal studies rely on the assumption that the process producing results also operates in humans. Meta-analyses assume the homogeneity of randomized trials under investigation. Similarly, the accusation that “mathematical models do not include value systems or morals” describes all research methods used in medicine or elsewhere. RCTs can inform us of the efficacy or safety of a drug in comparison to a control group, but they are neither suitable nor aimed at weighing the risk-reward ratio. Observational studies in epidemiology can deliver evidence that exposure is related to a negative outcome, but only nonepistemic values external to research can inform the decision if the potential benefit outweighs the (also non-financial) costs of limiting exposure.
How, therefore, should we assess the quality of evidence for the efficacy of mitigation and suppression measures delivered by epidemiological ABMs? Such models, considered as representing existing mechanisms [11], can be compared to laboratory research. The efficacy claims are internally valid as long as no coding or calculation error occurs (i.e., they accurately describe the effects of interventions within the model world). However, if the mechanisms represented by ABMs differ significantly from the process producing the outbreak that is targeted with the intervention under consideration or is influenced by factors external to the model, then such evidence, similarly to a significant number of laboratory studies, lack external validity. Unfortunately, considering the fact that RCTs are not feasible for assessing the efficacy of nonpharmaceutical interventions and the decisions need to be made before observational results will be accessible, decision-makers should consider the current best evidence and assess the external validity of epidemiological models in order to choose the study most relevant for their purpose.
References:
[1] Sridhar, D, Majumder, D. Modelling the pandemic. BMJ. 2020: 369:m1567. doi: https://doi.org/10.1136/bmj.m1567
[2] Pan A, Liu L, Wang C, Guo H, Hao X, Wang Q, Huang J, He N, Yu H, Lin X, Wei S. Association of public health interventions with the epidemiology of the COVID-19 outbreak in Wuhan, China. JAMA. 2020 Apr 10.
[3] Ghelichkhani P, Esmaeili M. Prone Position in Management of COVID-19 Patients; a Commentary. Archives of Academic Emergency Medicine. 2020;8(1).
[4] OCEBM Levels of Evidence Working Group. " The Oxford 2011 Levels of Evidence." Oxford Centre for Evidence-Based Medicine. http://www. cebm. net/index. aspx? o= 5653. 2011.
[5] National Institute for Health and Care Excellence. Developing NICE guidelines: the manual. https://www.nice.org.uk/media/default/about/what-we-do/our-programmes/de...
[6] Koo JR, Cook AR, Park M, Sun Y, Sun H, Lim JT, Tam C, Dickens BL. Interventions to mitigate early spread of SARS-CoV-2 in Singapore: a modelling study. The Lancet Infectious Diseases. 2020 Mar 23. https://www.thelancet.com/journals/lancet/article/PIIS1473-3099(20)30162-6/fulltext
[7] Giordano G, Blanchini F, Bruno R, Colaneri P, Di Filippo A, Di Matteo A, Colaneri M. A SIDARTHE model of COVID-19 epidemic in Italy. arXiv preprint arXiv:2003.09861. 2020 Mar 22.
[8] Adam D. Special report: The simulations driving the world's response to COVID-19. Nature. 2020 Apr 2. https://www.nature.com/articles/d41586-020-01003-6
[9] Ferguson N, Laydon D, Nedjati Gilani G, Imai N, Ainslie K, Baguelin M, Bhatia S, Boonyasiri A, Cucunuba Perez ZU, Cuomo-Dannenburg G, Dighe A. Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand. Imperial College London.
[10] Chang SL, Harding N, Zachreson C, Cliff OM, Prokopenko M. Modelling transmission and control of the COVID-19 pandemic in Australia. arXiv preprint arXiv:2003.10218. 2020 Mar 23.
[11] Clarke B, Gillies D, Illari P, Russo F, Williamson J. Mechanisms and the evidence hierarchy. Topoi. 2014 Oct 1;33(2):339-60.
The work of Mariusz Maziarz has received funding from the European Research Council (ERC) (grant agreement No 805498).
Competing interests: No competing interests
Dear Editor
The researchers from Singapore University of Technology and Design recently launched a website [1] presenting the predicted CoViD-19 end dates in various countries across the world. The predictions are based on susceptible-infected-recovered (SIR) model [2,3] that used the pandemic life cycle curves to predict the CoViD-19 end dates for various countries across the world. The model uses a normal distribution (a classical bell-shaped curve) in predicting expected end dates.
Interestingly, the distribution curves in many countries may not fit the Gaussian function as the CoViD-19 life cycle curves are not fully symmetric, i.e., "bell-shaped". The curves are asymmetric and mainly skewed to the right (positive skewness) which means the actual end dates can be much later than the current predictions that are based on the normal distribution. This is particularly evident in profiles in the United Kingdom where the statistical calculation of skewness came around 0.5 in our analysis. This means CoViD-19 may not end in the UK by the 28th May 2020 as the model currently predicts. A similar asymmetry is seen in several other countries including Italy, USA, Spain, Canada, UAE etc. The expected end date in the world is, therefore, also likely to be later than the predicted date using this model. Caution is necessary for any over-enthusiasm on the end of CoViD-19 based on these predictions.
Contrary to these, some other countries where the pandemic started late still seems to be on the upward trajectory of the predicted curves. Some interesting examples may include Saudi Arabia, Qatar, Bahrain etc. It is highly likely that these countries may not see the expected peaks predicted by the bell-shaped profiles, provided the early lock-down and effective track n trace measures were exercised. This may mean that these countries may benefit from a much earlier end of CoViD-19 than what's currently predicted by this model.
Undoubtedly, these profiles are significantly influenced by the lockdown and containment measures; any predicted end-date is associated with the current cycle of this pandemic. A second epidemic or relapse is not impossible that will have its own life cycle to end. Therefore, the absolute end of the pandemic may also depend on the availability of a vaccine or other preventive/therapeutic intervention to come due course. However, despite its limitations, as with any modelling approach, the model still provides a reasonable prediction of end dates in some countries but caution should be exercised in interpreting these curves as any oversimplification may be misleading for the policymakers and the public.
[1] Predictive Monitoring of COVID-19, Singapore University of Technology and Design. https://ddi.sutd.edu.sg/when-will-covid-19-end/
[2] The SIR Model for Spread of Disease - The Differential Equation Model. The Mathematical Association of America. https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread...
[3] fitVirusCOVID19: Estimation of coronavirus COVID-19 epidemic evaluation by the SIR model. https://uk.mathworks.com/matlabcentral/fileexchange/74658-fitviruscovid19
Competing interests: No competing interests
Re: Modelling the pandemic
Dear Editor,
In the recent editorial “Modelling the pandemic” [1] Devi Sridhar and Maimuna Majumder raised a number of issued related to the use of mathematical models in guiding the policy response(s) to the current pandemic. We agree both with the fact that the models have key limitations based on their necessary simplifying assumptions and also with the necessity of using models as a policy tool. In this response we want to argue that the predictive power of epidemiological models – and their utility as a policy tool – could be significantly improved through a more robust consideration of global socio-economic inequalities.
Much of the global debate on the contagion dynamics of COVID-19 relies upon projections developed through the use of compartmental epidemiological models. This approach divides a given population into relevant compartments – one common sub-division is between Susceptible, Infected, Recovered, and Deceased – and then models the probability of individuals moving between these compartments. Within this, an important policy focus has been the effectiveness of different combinations of non-pharmaceutical interventions (NPIs) in reducing the transition probability from Susceptible to Infected. A rapidly growing literature utilises compartmental models to analyse various factors influencing COVID-19’s transmission and fatality rates – this includes research into the impact of individual compliance with physical distancing measures, the timing and character of other NPIs, and the reliability and homogeneity of government data [2, 3, 4].
It is our contention, however, that global socio-economic inequalities, should be incorporated to these models. Socio-economic conditions determine the capacities of states to implement NPIs as well as the ability of populations to comply with them – they thus have a considerable effect on the transmission and fatality rates of COVID-19. This is particularly important for low-income countries, where poverty and inequality present significant obstacles to standard containment and mitigation measures derived from compartmental modelling.
One example of such socio-economic factors is the nature of work and employment. According to the OECD, around 70% of all employment in developing and emerging countries takes place in the informal sector, where labour is unregulated, intermittent, and poorly remunerated [5]. In these conditions, it is very difficult to enforce longer periods of lockdown and social isolation because the majority of the population depends upon immediate daily wages for survival and lack prior savings. Indeed, as part of their COVID-19 strategy for developing countries, the International Labour Organization has acknowledged that ‘physical distancing measures’ are an ‘impossible choice for informal economy workers’ [6].
A further example is the provision and quality of housing. An estimated one-quarter of the world’s urban population currently live in slums and other types of informal housing [7]. For some cities in the developing world, the proportion of people living in slums can reach up to 80% of the total population [8]. As with conditions of labour, such living arrangements present severe obstacles for those attempting to quarantine or self-isolate. Informal housing typically consists of multiple families sharing single dwellings, and intergenerational family units that can bring vulnerable populations into close contact with potential sources of infection. Shared infrastructures – including water, sewage and sanitation – present further potential vectors of infection, a problem exacerbated by high population densities and the poor quality of this infrastructure.
To be clear, this is not a criticism of modelling per se but a call for a more socially grounded and globally inclusive approach to these techniques. Socio-economic conditions such as those noted above bear directly on how many people get infected, how quickly these infections take place, the likelihood of dying, and the efficacy (and available choices) of NPIs. From the perspective of a compartmental epidemiological model, these social conditions shape the ‘transition rates’ between compartments, and it would be a relatively straightforward proposition to build an expanded model that incorporates these factors. Moreover, while our discussion has largely focused on differences between poorer and richer countries, the same approach could also be used to model the impact of socio-economic differentiation within individual countries.
There are numerous other socio-economic conditions that could (and should) be considered in developing such an expanded model – quality of health systems, gender inequalities, educational disparities, the prevalence of diseases associated with poverty, levels of government expenditure on social services, and so forth. Data on all of these indicators are widely available from government statistical agencies and multilateral development institutions and could be deployed in model simulations. Incorporating these factors into epidemiological models further strengthens the argument that poverty is an issue of public health and must be treated as such. It also echoes the recent call by Lancet Global Health editors for a decolonised approach towards COVID-19 [9]. In the face of a pandemic that has potentially very serious implications for the world’s poor, epidemiological models that foreground global inequality could make an important contribution to the immense public health challenges presented by COVID-19.
References
[1] Sridhar, D, Majumder, D. Modelling the pandemic. BMJ. 2020: 369:m1567. doi: https://doi.org/10.1136/bmj.m1567
[2] Prem, Kiesha et al. The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study. The Lancet Public Health, 2020; Volume 5, Issue 5, https://doi.org/10.1016/S2468-2667(20)30073-6
[3] Verity, Robert et al (2020) Estimates of the severity of coronavirus disease: a model-based analysis, The Lancet Infectious Diseases. 2020; Volume 20, Issue 6, 669 – 677
https://doi.org/10.1016/S1473-3099(20)30243-7
[4] Baskozos, G., Di Guilmi, C. and Galanis, G. Social distancing and contagion in a discrete choice model of COVID-19, University of Warwick, Centre for Research in Economic Theory and its Applications, Discussion Papers Series, 2020
[5] OECD/ILO (2019), Tackling Vulnerability in the Informal Economy, Development Centre Studies, OECD Publishing, Paris, https://doi.org/10.1787/939b7bcd-en.
[6] International Labour Organization (ILO). Rapid assessment of the impact of COVID-19 on enterprises and workers in the informal economy in developing and emerging countries. https://www.ilo.org/global/topics/employment-promotion/informal-economy/...
[7] Habitat for Humanity. The World’s Largest Slums. 2020; https://www.habitatforhumanity.org.uk/blog/2017/12/the-worlds-largest-sl...
[8] WHO. Health and Sustainable Development: Slum Upgrading. 2020; https://www.who.int/sustainable-development/cities/strategies/slum-upgra...
[9] The Lancet Global Health. Decolonising COVID-19. The Lancet Global Health. 2020; volume 8, Issue 5. https://doi.org/10.1016/S2214-109X(20)30134-0
Competing interests: No competing interests