Solution to Century-Old Math Problem Could Predict Transmission of Infectious Diseases

The finding has far-reaching implications across a range of disciplines and possible applications include predicting molecules diffusing inside cells.  (Image: via   pixabay  /  CC0 1.0)
The finding has far-reaching implications across a range of disciplines and possible applications include predicting molecules diffusing inside cells. (Image: via pixabay / CC0 1.0)

A Bristol academic has achieved a milestone in statistical/mathematical physics by solving a 100-year-old physics problem — the discrete diffusion equation in finite space. The long-sought-after solution could be used to accurately predict encounter and transmission probability between individuals in a closed environment, without the need for time-consuming computer simulations.

The finding has far-reaching implications across a range of disciplines and possible applications include predicting molecules diffusing inside cells, bacteria roaming in a petri dish, animals foraging within their home ranges, or robots searching in a disaster area. (Image: via pixabay / CC0 1.0)

The finding has far-reaching implications across a range of disciplines and possible applications include predicting molecules diffusing inside cells, bacteria roaming in a petri dish, animals foraging within their home ranges, or robots searching in a disaster area. (Image: via pixabay / CC0 1.0)

In his paper, published in Physical Review X, Dr. Luca Giuggioli, from the Department of Engineering Mathematics at the University of Bristol, describes how to analytically calculate the probability of occupation (in discrete time and discrete space) of a diffusing particle or entity in a confined space — something that until now was only possible computationally. Dr. Giuggioli said:

The finding has far-reaching implications across a range of disciplines and possible applications include predicting molecules diffusing inside cells, bacteria roaming in a petri dish, animals foraging within their home ranges, or robots searching in a disaster area. It could even be used to predict how a pathogen is transmitted in a crowd between individuals.

The long-sought-after solution could be used to accurately predict encounter and transmission probability between individuals in a closed environment, without the need for time-consuming computer simulations. (Image: via pixabay / CC0 1.0)

The long-sought-after solution could be used to accurately predict encounter and transmission probability between individuals in a closed environment, without the need for time-consuming computer simulations. (Image: via pixabay / CC0 1.0)

Solving the conundrum involved the joint use of two techniques: special mathematical functions known as Chebyshev polynomials and a technique invented to tackle electrostatic problems, the so-called method of images. This approach allowed Dr. Giuggioli to construct hierarchically the solution to the discrete diffusion equation in a higher dimension from the one in lower dimensions.

Provided by: University of Bristol [Note: Materials may be edited for content and length.]

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