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A mathematical perspective of seasonal variations in Lyme disease transmission
Date:12/19/2013

s active in colder temperatures, and rainfall is also critically important for their development, survival, and activities," explains author Xiao-Qiang Zhao. "According to a report from the Public Health Agency of Canada on Lyme disease cases in Ontario between 1999 and 2004, most occurred in late spring and summer, when the young ticks are most active and people are outdoors more often."

A previous model proposed a reaction and diffusion model to study global dynamics of Lyme disease. A reaction-diffusion model takes into account the interaction (reaction) of constituents within the system (in this case pathogens, susceptible hosts and infective hosts) and their change in density over time within their respective populations (diffusion).

The previously-proposed spatial model treats population densities in a continuous two-dimensional space, factoring in birth, death, infection and developmental advancement. However, the model does not account for seasonal patterns.

In this paper, the authors modify this previous model into a reaction and diffusion model in a periodic environment, which models seasonable variables (eg. temperature) as a periodic function. A periodic function is one that repeats its values at regular intervals.

Since seasonal variations are critical for tick development and their activities, which are strongly affected by temperatures, the authors assume that the development rates of ticks as well as their activity rates are time-dependent. The model is governed by a periodic reaction-diffusion system that factors in the densities of susceptible and pathogen-infected mice, densities of susceptible and infectious larvae and nymphs, and densities of uninfected and pathogen-infected adult ticks.

The authors introduce the basic reproduction number R0, which is the number of infectious cases one case of disease can generate on average over the course of the infectious period in a susceptible population. The authors
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Contact: Karthika Muthukumaraswamy
karthika@siam.org
267-350-6383
Society for Industrial and Applied Mathematics
Source:Eurekalert  

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