**Computational & Systems
Neuroscience Laboratory
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Monash Biomedical Imaging

Monash University, Melbourne, Australia

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K. J. Friston,
T. Parr, P. Zeidman, **A. Razi**, G. Flandin, J. Daunizeau, O Hulme,
A. Billig, V. Litvak, R. J. Moran, C. J. Price, C.
Lambert, (2020) ``Dynamic causal modelling of COVID-19’’, ** arXiv**.

**Here** is
the accompanying website which hosts open access software code, among other
resources.

**Dynamic causal modelling: The generative
model**

This
figure is a schematic description of the generative model used in subsequent
analyses. In brief, this compartmental model generates timeseries data based on
a mean field approximation to ensemble or population dynamics. The implicit
probability distributions are over four latent factors, each with four levels
or states. These factors are sufficient to generate measurable outcomes; for
example, the number of new cases or the proportion of people infected. The
first factor is the location of an individual, who can be at *home*, at *work*,
in a critical care unit (*CCU*) or in the *morgue*. The second factor
is infection status; namely, *susceptible* to infection, *infected*, *infectious*
or *immune*. This model assumes that there is a progression from a state
of susceptibility to immunity, through a period of (pre-contagious) infection
to an infectious (contagious) status. The third factor is clinical status;
namely, *asymptomatic*, *symptomatic*, *acute respiratory distress syndrome (ARDS)* or *deceased*.
Again, there is an assumed progression from asymptomatic to ARDS, where people
with ARDS can either recover to an asymptomatic state or not. Finally, the
fourth factor represents diagnostic or testing status. An individual can be *untested*
or *waiting* for the results of a test that can either be *positive*
or *negative*.

With
this setup, one can be in one of four places, with any infectious status,
expressing symptoms or not, and having test results or not. Note that—in this
construction—it is possible to be infected and yet be asymptomatic. However,
the marginal distributions are not independent, by virtue of the dynamics that
describe the transition among states within each factor. Crucially, the
transitions within any factor depend upon the marginal distribution of other
factors. For example, the probability of becoming infected, given that one is
susceptible to infection, depends upon whether one is at home or at work.
Similarly, the probability of developing symptoms depends upon whether one is
infected or not. The probability of testing negative depends upon whether one
is susceptible (or immune) to infection, and so on. Finally, to complete the
circular dependency, the probability of leaving home to go to work depends upon
the number of infected people in the population, mediated by social distancing.
The curvilinear arrows denote a conditioning of transition probabilities on the
marginal distributions over other factors. These conditional dependencies
constitute the mean field approximation and enable the dynamics to be solved or
integrated over time. At any point in time, the probability of being in any
combination of the four states determines what would be observed at the
population level. For example, the occupancy of the deceased level of the clinical
factor determines the current number of people who have recorded deaths.
Similarly, the occupancy of the positive level of the testing factor determines
the expected number of positive cases reported. From these expectations, the
expected number of new cases per day can be generated.

**Dynamic causal modelling of Australian COVID-19
data**

We
have used this DCM to model and provide projections for new cases and
fatalities in Australia in the wake of the COVID-19 spread. We used the data
provided by **JHU CSSE** (data until 6^{th}
April). The results of this analysis are made available to showcase the
modelling. They should not be taken seriously as a prediction. This is because
the current cases are extremely small in number; violating the large number
assumption that underwrites the likelihood model used in the DCM.
Operationally, countries with cumulative deaths of less than 128 are usually
excluded from the hierarchical (parametric empirical Bayesian) modelling – when
testing for systematic between country differences. In one sense, if a country
suffers a very small number of deaths, it can be, effectively, considered as
having eluded the pandemic.

Figure 1 reports predicted new deaths and cases (and CCU occupancy) for
Australia. The panels on the left show the predicted outcomes as a function of
weeks. The blue lines correspond to the expected trajectory, while the shaded
areas are 90% Bayesian credible intervals. The black dots represent empirical
data, upon which the parameter estimates are based. The lower right panel shows
the parameter estimates. As in previous figures, the prior expectations are
shown as pink bars over the posterior expectations (and credible intervals).
The upper right panel illustrates the equivalent expectations in terms of
cumulative deaths.

In Figure 2, the upper panels reproduce the expected trajectories for
Australia. The expected death rate is shown in blue, new cases in red,
predicted recovery rate in orange and CCU occupancy in yellow. The black dots
correspond to empirical data. The (zoomed) square box on upper right panel
shows the cumulative deaths otherwise not obvious. The lower four panels show
the evolution of latent (ensemble) dynamics, in terms of the expected
probability of being in various states. The first (location) panel shows that
after about 10 weeks, there was a sufficient evidence for the onset of an
episode (we are past that peak) that induced social distancing, such that the
probability of being found at work falls, over a couple of weeks to negligible
levels. At this time, the number of infected people increases (approx. 0.5%)
with a concomitant probability of being infectious a few days later. During
this time, the probability of becoming immune increases monotonically and
saturates at about 20 weeks. Clinically, the probability of becoming
symptomatic rises to about 0.4%, with negligible probability of developing
acute respiratory distress (ARDS) and, possibly death (these probabilities are
very small and cannot be seen in this graph). In terms of testing, there is a
progressive increase in the number of people tested, with a concomitant
decrease in those untested or waiting for their results. Under these
parameters, the entire episode lasts for about 10 weeks, or less than three
months.

Dynamic causal modelling of COVID-19 spread across regions

Subsequently, we combine several of these
(epidemic) models to create a (pandemic) model of viral spread among regions.
Our focus is on second wave of new cases that may result from loss of immunity—and
the exchange of people between regions—and how mortality rates can be
ameliorated under different strategic responses. In particular, we consider hard
or soft social distancing strategies predicated on national (Federal) or regional
(State) estimates of the prevalence of infection in the population.

K. J. Friston, T. Parr, P. Zeidman, **A. Razi**, G. Flandin, J. Daunizeau,
O Hulme, A. Billig, V.
Litvak, R. J. Moran, C. J. Price, C. Lambert, (2020) ``Second waves,
social distancing, and the spread of COVID-19 across America’’, ** arXiv**.
Link.

**Review on Data Science and COVID-19**

We have also written a comprehensive review in an attempt to systematise
ongoing data science activities in this area. As well as reviewing the rapidly
growing body of recent research, we survey public datasets and repositories
that can be used for further work to track COVID-19 spread and mitigation
strategies.

S. Latif, M. Usman, S. Manzoor, W. Iqbal, J. Qadir, G Tyson, I. Castro, **A.
Razi**, M. N. K. Boulos, and J. Crowcroft, ``Leveraging data science to
combat COVID-19: A comprehensive review”, **Link**

**Here**
is the accompanying website which is constantly updated with new datasets and
other community resources.