E267A: Modeling and simulation of infectious diseases-the cutting edge: microscale transmission, decontamination and macroscale propagation

The course emphasizes elementary modeling, numerical methods and their implementation on physical problems motivated by real-world phenomena that students are likely to encounter in their careers.

Part 1: Microscale Transmission: modeling and simulation of the  infection zone from a  cough

The pandemic of 2020 has led to a huge  interest  of modeling and  simulation of infectious diseases.    One of the central questions is the potential infection zone produced by a  cough.  In this part of the course,  mathematical models are developed to simulate the progressive time-evolution of  the  distribution of  particles  produced by a cough.  Analytical and numerical studies are undertaken.  The models ascertain the range, distribution and settling time of the particles under the influence of gravity and  drag from the surrounding air. Beyond qualitative trends that conclude that large particles  travel far and settle quickly, while small particles do not travel far and settle slowly, the models provide quantitative results for distances travelled and settling times, which would be needed for constructing  social distancing policies and workplace protocols.

Part 2: Decontamination:Rapid simulation of viral decontamination efficacy with UV irradiation

The pandemic of 2020 has led to a dramatic increase in  research in the area of modeling and  simulation  of infectious diseases.  This part of the course focuses on decontamination by ultraviolet “UV-C” irradiation technologies and  develops an efficient  and rapid computational method to simulate a UV pulse in order to ascertain the decontamination efficacy  of UV irradiation for a surface. It is based on decomposition of a pulse into a groups of rays, which are  then tracked as they progress towards the target contact surface. 
The algorithm computes the absorption  at the  point of contact and color codes it relative to the  incoming irradiation.  This allows one to  quickly quantify the decontamination efficacy  across the topology of the structure.

Part 3: Macroscale Propagation:Pandemic on Planet X: an agent-based  computational framework for simulation for global pandemics


The increase in readily available computational power raises the possibility that direct  agent-based modeling can play a key  role  in the analysis of epidemiological population dynamics. Specifically,  the objective of this part of the course  is to develop a robust agent-based computational framework  to   investigate the emergent structure of SIR-type  (Susceptible-Infected-Removed) populations   on a global planetary  scale. Specifically, we develop   a planet-wide  model based on interaction between discrete entities (agents), where   each agent  on the surface of the planet is  initially uninfected. Infections are then seeded on the planet in localized regions.   Contracting an infection (susceptibility) depends on the characteristics   of each agent (they have different morbidities, genders, genetic predispositions, etc) and contact  with    the seeded, infected, agents. Agent  mobility   on the planet is dictated by policies, for example such as “shelter in place”,  “complete lockdown”, etc.  The global population is then  allowed to evolve according to infected states of agents  over many    generations, leading to an SIR population.  The work illustrates the construction of the computational framework and  the relatively straightforward  application, with direct, non-phenomenological input    data.   Numerical examples are provided to illustrate the model construction and the results  of such an approach.