Discrete and algorithmic mathematics in biology and epidemiology - Part I
Org: Pengyu Liu
(Simon Fraser University)
- XINGRU CHEN, Dartmouth College
Effectiveness of Massive Travel Restrictions on Mitigating Outbreaks of COVID-19 in China [PDF]
In the early stage of an outbreak of COVID-19 started in the epicenter, Wuhan, Hubei Province, the Chinese government imposed by far the largest scale of travel restrictions nationwide, amid the busiest period for domestic travels during the Lunar New Year. Such massive restrictions have caused a dramatic reduction in travel volume and helped curb the imported cases to other provinces. The control measures could slow down the onset of epidemic outbreaks and weaken the impact of the disease. We are interested in estimating the effectiveness of massive travel restrictions on the mitigation of disease impact using a data-driven approach.
- BAPTISTE ELIE, MIVGEC, Université Montpellier
The source of individual heterogeneity shapes infectious disease outbreaks [PDF]
Studies show that the biological sources of heterogeneity affects
epidemic spread, but they do so without controlling for the overall
heterogeneity in the number of secondary cases caused by an infection.
Here, we control for this important bias to explore the role of
individual variation in infection duration and transmission rate on
parasite emergence and spread. Our results show that using realistic
distributions for infection duration is necessary to accurately capture
the effect of individual heterogeneity on epidemiological dynamics,
which has implications for the monitoring and control of infectious
diseases, as well as data collection.
- WASIUR KHUDABUKHSH, Ohio State University
Chemical reaction networks with covariates [PDF]
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics, Markov models that require exponentially distributed inter-event times have been used widely. However, some biophysical processes are known to render the usual exponential assumption untenable. We relax this assumption by incorporating age-dependent random time delays into the system dynamics. We do so by constructing a measure-valued Markov process whose large-volume limiting density can be approximated by Partial Differential Equations (PDEs). We show how the limiting PDE system can be used for the purpose of devising efficient simulation algorithms.
- JOEL MILLER, La Trobe University
Simulating epidemic spread on contact networks [PDF]
Simulation of disease spread in contact networks is more challenging than in well-mixed populations because the simulation needs to track more than just how many individuals have each infection status, but also, which specific individuals have each infection status. So standard simulation approaches may be significantly slowed by the extra effort required to identify which individual is changing status each time an event occurs. In this talk I will discuss algorithms which allow us to efficiently simulate infection spread in (static) contact networks, and offer an introduction to the Python Epidemics on Networks (EoN) package.