Epidemics are spatial, stochastic, and wireless

Inspired by current events, let us focus on the “successful” transmission of a virus from one host to another. In the case of a coronavirus, such transmission happens when the infected person (the source) emits a “signal” by breathing, coughing, sneezing, or speaking, and another person (the destination) gets infected when the respiratory droplets land in the mouth or nose or are inhaled. Fundamentally, the process looks very similar to that of a conventional RF wireless transmission. There are notions of signal strength, directional transmission, path loss, and shadowing in both, resulting in a probability of “successful” reception. In both cases, distances play a critical role – there is the well-known 2 m separation in the case of coronaviral transmission that (presumably) causes an outage in the transmission with high probability; similarly, in the wireless case, there is sharp decay of reception probabilities as a function of distance due to path loss.

Given the critical role of the geometry of host (transceiver) locations, it appears that known models and analytical tools from stochastic geometry could be beneficially applied to learn more about the spread of an epidemic. In contrast to the careful modeling of channels and transmitter and receiver characteristics in wireless communications, the models for the spread of infectious diseases are usually based on the basic reproduction number R0, which is a population-wide parameter that reflects distances between individual agents very indirectly only. Since it is important to understand the effect of physical (Euclidean) distancing (often misleadingly referred to as “social distancing”) and masking (i.e., shadowing), it seems that incorporating distances explicitly in the models would increase their predictive power. Such models would account for the strong dependence of infection probabilities on distance, akin to the path loss function in wireless communications, as well as directionality, akin to beamforming. Time of proximity or exposure can be incorporated if mobility is included.

This line of thought raises some vital questions: How can expertise in wireless transmission be applied to viral transmission? What can stochastic geometry contribute to the understanding of how infectious diseases are spreading (spatial epidemics)? Is there a wireless analogy to “herd immunity”, perhaps related to percolation-theoretic analyses of how broadcasting over multiple hops in a wireless network leads to a giant component of nodes receiving an information packet?

I believe it is quite rewarding to think about these questions, both from a theoretical point of view and in terms of their real-world impact.

Papers on these topics are solicited in the special issue on Spatial Transmission Dynamics of MDPI Information (deadline Feb. 28, 2021).

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