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Guide to Epidemiological Modelling of Covid-19

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An in-depth guide drawing on our work with the Covid-19 International Modelling Consortium (CoMo) and the University of Oxford

The World Health Organisation Eastern Mediterranean Regional office describes infectious disease modelling with the analogy of a weather forecast; they project potential future scenarios based on past experiences and currently available data.

Since mid-March, when the World Health Organisation announced that covid-19 had officially grown to pandemic proportions (1), many countries around the world implemented various degrees of lockdowns to mitigate the spread of the disease. As there is no vaccine currently available, governments are forced to rely on behaviour change strategies such as handwashing, social distancing, and school closures, which are commonly referred to as non-pharmaceutical interventions (NPIs), to reduce the disease transmission within their population. The approaches that each government have taken are as varied and diverse as the contexts they are implemented in. For instance, the United Kingdom implemented a nation-wide lockdown, which included closing schools and forbidding any form of social gatherings or non-essential travel, among other NPIs (2). In contrast, Sweden took a different approach, allowing primary schools and restaurants to remain open, but still encouraging people to work from home when they could (3).

In the context of many low and middle income countries (LMICs), governments are aware of the risk the disease poses to their population, with many implementing strict lockdowns at very early stages of the epidemic (4,5). India implemented a nation-wide lockdown starting on the 25th of March (6), prohibiting all non-essential travel and social gatherings. Initially, the lockdown was intended to last for three weeks, however the government found it necessary to continuously extend the strategy for weeks at a time. The economic stress caused by the government’s response has been substantial, with millions of people losing their jobs (7). In contrast, Sierra Leone tried to strike a balance between the economic and disease burden, intermittently locking the country down for three days every few weeks, while easing restrictions when the lockdown was not in place (8).

Benefits of Infectious Disease Modelling

The varied responses governments have taken to combating the disease raises the question: what is the most effective combination of interventions to mitigate the transmission of the disease in a particular country? Infectious disease models are best poised to answer this question and others, such as when a country will most likely observe the peak in the disease burden and the total number of deaths projected to occur under a particular strategy. It is important to consider context-specific strategies, as there is no one-size-fits all approach.

What are infectious disease models?

Many people have different definitions for infectious disease modelling, but they may broadly be described as the mathematical or logical representation of the epidemiology of an infectious disease (9). There are many different types of epidemiological models, each with their own specific purposes, data and set of accompanying assumptions (10). However, they may broadly be categorized into distinct classes: mechanistic models, statistical models, and risk prediction models. These are described below (9):

  • Mechanistic disease models may be used to estimate the long-term burden of the disease, incorporating assumptions relating to the mechanism of transmission.
  • Statistical disease models are typically used to predict the short-term incidence of the disease, taking into account the spatial distribution of the disease cases. It is important to make the distinction between mechanistic and statistical models that the latter do not include any assumptions around the transmission mechanism through which the disease spreads, and therefore is not suited to make long-term predictions of the disease burden.
  • Risk models assess the risk of a disease outbreak occurring in a population or location of interest.

Here, we focus particularly on mechanistic infectious disease models. OPM has been working with a mechanistic infectious disease model, developed by the COVID-19 International Modelling Consortium (CoMo) to estimate the burden of the disease.

Covid-19 International Modelling Consortium

OPM is a member of the COVID-19 International Modelling Consortium (CoMo). CoMo is a team of international researchers, mathematical modellers, epidemiologists and local in-country experts committed to developing data-informed policies aimed at mitigating the burden of covid-19. The CoMo model is a mechanistic, compartmental Susceptible-Exposed-Infectious-Recovered (SEIR) disease model (11). Compartmental models separate the population of interest into various compartments, representing the progression and severity of the disease within an individual (10). As the fatality of the disease is heavily dependent on the age of a person (12), the model separates the population further with respect to age.

How the CoMo model captures the transmission of the disease within a population

The covid-19 virus is transmitted through the exchange of infected fluid droplets between an infected person and someone who is still susceptible to it (13). The exchange of the infected droplets from person-to-person may happen through several routes, such as: being in close proximity to someone who is sneezing or coughing, touching a surface that was recently touched by an infected person, or through physical contact with an infected individual. Modelling each of the routes between individual people at a population scale is not only difficult, but impractical. To circumvent this issue, the CoMo model uses the rate at which two people come into (either physical or non-physical) contact with each other as a proxy for the probability of transmission of the virus. Estimates for the contact rate between people in different settings (such as work, home or school, etc.) and ages are available and nationally represented for 152 countries (14). This approximation in the model brings many assumptions along with it, most notably that the population of interest, disaggregated into specific age groups, is assumed to be homogenous. It should be noted that this is an assumption broadly associated with compartmental models, in that people in a particular age group are assumed to all have the same characteristics, such as the rate at which they come into contact with other people, and their individual susceptibility to the disease. However, as the purpose of the CoMo model is to estimate the burden of the disease across a population, this assumption is necessary. Accounting for heterogeneity within a population is possible, but would require significantly more data such as the locations and frequency which individual people typically travel on their daily commute, which is inaccessible, if not unavailable, in many LMICs.

Assumptions relating to Non-Pharmaceutical Interventions

The CoMo model is able to estimate the impact of various interventions, including handwashing, social distancing, and self-isolation of infected individuals. However, assessing the impact an intervention will have, requires estimating the coverage and adherence of the respective interventions. Coverage may be thought of as the percent of people in a population who comply with a particular intervention, and adherence is a measure for the degree of compliance for those who incorporate the intervention rules into their lives (15). In many contexts, due to the restrictions of movement placed on people, it has been impossible to conduct surveys that aim to quantitatively evaluate the coverage and adherence of the various NPIs. So as a substitute, the CoMo consortium relies on local knowledge and expertise to gauge these parameters.

Accounting for under-reporting of cases

To ensure the CoMo model is relevant and accurate to the context, the model is calibrated so that the estimated incidence (number of new cases per day) predicted from the model resembles the reported incidence for the region under question. However, the reported incidence may be significantly different from the true incidence which is needed to estimate the true rate of transmission of the disease in a population. However, the true incidence is difficult to estimate, as it requires an efficient and expansive screening facilities, which many countries, including high-income countries, do not have the capacity to support (16). Countries such as South Korea and Iceland were able to implement aggressive testing and contact tracing schemes swiftly, allowing them to accurately estimate the prevalence of the disease in their respective populations (17,18), and thus allowing them to implement highly targeted interventions. Senegal swiftly implemented a national covid-19 response plan in early January, including contact tracing of suspected cases (19). Similarly, the Ghana Health Service, supported by a mass of volunteers and community health workers, implemented an extensive contact tracing plan (ibid). In East Africa, the Ethiopian government conducted a comprehensive door-to-door survey in Addis Ababa, documenting the travel history and symptoms of the city’s residents, and tracing the contacts of those suspected of being infected (20).

However, for the majority of LMICs, such interventions are difficult to execute, due to a relative absence of infrastructure to accurately estimate the prevalence of the disease. This is especially true as the number of cases becomes unmanageable, and the outbreak grows into an epidemic. The UK is finding it challenging to accurately estimate the number of people who have actually been infected with the disease (21,22), as the government has directed people who exhibit mild symptoms of covid-19 to isolate themselves at home, and only to seek healthcare if they exhibit severe symptoms (23).  

Due to the uncertainties that surround the true disease incidence in a country, it is imperative to incorporate a measure of under-reporting of new cases. However, as with other parameters, this is difficult to estimate. For this, CoMo relies on local expertise and knowledge to gauge the under-reporting rate. It is also worth noting, at the peak of the epidemic when the healthcare system is most severely overburdened, it is likely that most mild and asymptomatic cases may go unreported. As an example, the city of Wuhan in China added 1,290 deaths due to covid-19 when they revised their official estimate (24) in late March 2020, bringing the official death total in China at the time of writing to 4,638. Similar issues of underreporting have been observed in other locations, including New York, USA, which added nearly 3,700 deaths from people suspected of having covid-19, but who were never tested (25).

Uncertainty around disease severity

Little is known about the severity of the disease. Calculating the infection-fatality rate (IFR) - the rate at which people in each age group could be expected to die from the disease assuming they are infected - with any accuracy is very difficult. Although estimates for the infection-fatality rate exist (12), there is significant uncertainty around them, as both the true number of infected people and the actual number of deaths caused by covid-19 is not accurately known (26). Assuming a large population of asymptomatic cases exist but have not been reported, a highly plausible scenario given the under-reporting rates in many countries, The Economist theorises the IFR is an order of magnitude less than many estimates (27). It is also important to note the IFR is dependent on many other factors, not least the state of health care in a country, and the degree by which the healthcare system is over-burdened. This uncertainty compounds further complexity to modelling the disease and the burden it places on communities.

Data Requirements for the CoMo model

We briefly discuss parameters the model uses to estimate the disease burden, the information the model is able to provide, and areas of future development. The main parameters to the CoMo model include:

  • Demographic population estimates disaggregated by age
  • The social contact patterns representative of a population
  • A timeline of confirmed cases and deaths attributed to covid-19 in the context of interest
  • A timeline of interventions that have been implemented to-date, alongside estimates for the coverage and adherence of those interventions.

Most of the above data is freely available and easily accessible at a national level. Carrying out this analysis at a sub-national scale, at city or provincial level, could prove to be extremely useful to policymakers as it would allow for more targeted interventions relevant to the context which they are implemented in. A subnational analysis of a city or a particular region is feasible using the CoMo model, provided the data described above for the region of interest is available for the modellers to use.

Provided the above data sources are made available, the CoMo model is able to estimate:

  • The impact of the various mitigation strategies on transmission of the virus and mechanisms for “flattening of the curve” and which interventions will be more effective in their specific contexts
  • The anticipated demand for hospital and ICU beds at various levels of the health system
  • The quantity of tests, personal protective equipment, ventilators and other supportive tools needed in treating the diagnosis and treatment of patients
  • The cost of equipment needed.

Further developments are being made to the CoMo model, adding complexity to it in new and different ways, including accounting for comorbidities (such as chronic kidney disease, obesity, serious heart condition or type II diabetes (28)), and estimating the spatial distribution of the disease at sub-national levels, and incorporating an economic analysis of the impact of various intervention strategies.

Summary

We have described the general concepts that surround infectious disease modelling, the questions it is capable of answering, and the uncertainty involved in the modelling process. Given the significant burden covid-19 has had on the world to date, infectious disease modelling has proven to be highly relevant to policymakers, helping identify the most effective interventions to mitigate the spread of the disease, predicting when the peak of the disease might occur, and the projected economic costs of the interventions. Even now, when many countries are removing NPI’s, epidemiologically modelling remains as relevant as ever. Epidemiological modelling can be used to identify appropriate processes to maintaining safe public health measures while easing restrictions and preventing a second wave of infections. For these reasons, it is important for policymakers to understand the assumptions these models make, and the uncertainty in their estimates. We emphasise that although it is highly relevant to the current context in many countries, it is one tool out of many that are at the disposal of policymakers and governments. Other tools that may be of use to policymakers include (but not limited to):

  • hotspot analysis, where researchers identify areas of high transmission risk;
  • call detail records which, through the use of mobile phones, allows researchers to access the degree of adherence people obey social distancing interventions and restrictions on travel;
  • although it requires significant resources and testing kits to be available, contact tracing is a highly effective measure to containing the spread of the disease at the very earliest stages.

The World Health Organization Eastern Mediterranean Regional office describes infectious disease modelling with the analogy of a weather forecast; they project potential future scenarios based on past experiences and currently available data (29).

This article also describes the key assumptions made by the CoMo model, the core data sources it uses, and the estimates it is able to provide. The assumptions made by the CoMo model are characteristic of mechanistic compartmental disease models. For this reason, it is important to stress that disease models should be interpreted as an approximate “order-of-magnitude” calculation of which there is significant degree of uncertainty around. Given the vulnerability of many LMICs, both in terms of the human and economic repercussions of covid-19, governments must carefully choose the interventions they implement to mitigate the effects of the disease, taking into consideration the contexts in which they operate. It is the aim of infectious disease modelling to assist in the development of robust evidence-informed policies.

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