Disease spread
Introduction
By considering a model where the simulated agents represent individuals in a given community, the PiXIE environment can be extended to study how a virus can spread through the population. This can be achieved in a couple of ways, via either a physics-based approach or an activity-based model.
Physics-based model
In the animation below (Fig. 1), each individual in the population is represented as a bouncing ball with an associated epidemiological state that tracks its current stage of infection in the epidemic cycle. This state can evolve based on the agent’s interactions with its neighbours. The SIR (Susceptible, Infected, Recovered) epidemiological model is used here to represent the virus spread, meaning that an agent can be either Susceptible to the virus (that is, it had never been infected, and it can become infected if in contact with an infectious agent), Infected by the virus (and infectious as a result, after a set incubation period) or Recovered (and assumed immune as a result).
Figure 1. Modelling a population as a collection of bouncing balls interacting with each other.
This type of modelling is useful to visually represent the spread of a virus in a given population and to qualitatively show the effect of potential mitigation measures to slow down the progression of the disease (which can be modelled for example by a reduced risk of being infected if in contact with an infectious agent).
However such an approach is only suitable to build an idealized representation of a given population without incorporating any geospatial information into the model.
Activity-based model
In this second modelling strategy, the interactions between agents are simulated through daily activities, as opposed to physical movements. The core functionalities of PiXIE (neighbour search algorithm, processing of interactions) are retained to build the model, but now at each time step the location of each agent is updated from its daily plan of activities and no longer by integrating its equation of motion in time. An agent can then become infected if it comes into a contact with an infectious agent through one of its daily activities, as illustrated in Fig. 2.
Figure 2. Modelling the spread of a virus in PiXIE using an activity based model.
This model requires more input data than the physics-based model representing individuals as bouncing balls, as not only do we need to assign some characteristics to the agents (such as their age, to determine their daily routine), we now also require geospatial data to capture their activities throughout the day. However, assuming such data is available, or can be inferred from sources such as census surveys, this modelling is more powerful as it allows to build a potentially very accurate model of a community of interest (the only limitation being in the availability of the input data).
Using this approach it becomes possible to investigate in details the effectiveness of different interventions such as lockdowns (global or localized) or social measures (e.g. social distancing). Fig. 3 and Fig. 4 illustrate this point by showing the difference in the daily evolution of an epidemic in a population where no intervention has taken place (Fig.3) vs. where a lockdown, as well as social measures were imposed (Fig. 4). In this second scenario a second wave was also predicted in this particular case, after the lockdown has ended and the social measures are no longer followed by the population.
Figure 3. Disease spread in a population not subjected to lockdown measures. Top left: Evolution of the S,I,R population with time. Top right: places where infections have taken place. Bottom left: Daily new cases and cumulative number of cases with time. Bottom right: average daily number of contacts per person.
Figure 4. Disease spread in a population subjected to a 4-week lockdown and social measures from day 40, and occurrence of a second wave after the lockdown has ended and social measures are relaxed. Top left: Evolution of the S,I,R population with time. Top right: places where infections have taken place. Bottom left: Daily new cases and cumulative number of cases with time. Bottom right: average daily number of contacts per person, which shows the decrease in number of daily contacts due to the lockdown measures.