# 2018 Annual Meeting of the Society for Mathematical Biology & the Japanese Society for Mathematical Biology

8-12 July 2018
Australia/Sydney timezone

## Understanding the influence of tick co-aggregation on R0 for tick-borne pathogens

9 Jul 2018, 18:00
2h
Holme Building/--The Refectory (University of Sydney)

### Holme Building/--The Refectory

#### University of Sydney

20
Board: 215
Poster Presentation Disease - infectious

### Speaker

Simon Johnstone-Robertson (RMIT)

### Description

Tick-borne pathogens are transmitted when ticks take blood meals from vertebrate hosts. Ticks need to take blood meals to progress through immature life-stages and reach adulthood. For the most important zoonotic pathogens, including Borrelia burgdorferi (the causative agent of Lyme disease), two immature life-stages of the tick vector, termed larvae and nymphs, maintain the pathogens. Key features of tick feeding behaviour, and therefore of tick-host contact patterns, include the aggregation of ticks on hosts (whereby most ticks of a given life-stage feed on only a small minority of the hosts) and the co-aggregation of larval and nymphal ticks on the same minority of hosts.

A mechanistic network model is presented for tick-borne pathogen transmission that explicitly accounts for larval and nymphal tick co-aggregation and coincident coaggregation, also known as co-feeding. Co-feeding of nymphs and larvae allows transmission from an infected nymph to susceptible larvae feeding in close proximity and at the same time, but without the involvement of a systemic infection in the vertebrate host. By relating the next generation matrix epidemic threshold parameter $R_{0}$ to the in- and out-degrees of vertebrate host nodes in the mechanistic network model, a simple analytic expression for $R_{0}$ that accounts for the co-aggregation and coincident coaggregation of ticks is derived. Simulations of Lyme disease transmission on finite realizations of tick-mouse contact networks are used to visualize the relationship between $R_{0}$ and the extent of tick co-aggregation.

The derived analytic equation explicitly describes the relationship between $R_{0}$ and the strength of dependence between counts of larvae and counts of nymphs on vertebrate hosts. Tick co-aggregation always leads to greater values for $R_{0}$, whereas higher levels of tick aggregation only increases the value of $R_{0}$ when larvae and nymphs also co-aggregate. Aggregation and co-aggregation have a synergistic eﬀect on $R_{0}$ such that their combined eﬀect is greater than the sum of their individual eﬀects. Co-aggregation has the greatest effect on $R_{0}$ when the mean larval burden of hosts is high and also has a larger relative eﬀect on the magnitude of $R_{0}$ for pathogens sustained by co-feeding transmission (e.g. TBE virus in Europe) compared with those predominantly spread by systemic infection of the vertebrate host (e.g. Lyme disease).

Co-aggregation increases $R_{0}$, particularly in geographic regions and seasons where larval burden is high and for pathogens that are mainly transmitted during co-feeding. For all tick-borne pathogens though, the eﬀect of co-aggregation can be to lift $R_{0}$ above the threshold value of 1 and so lead to persistence.

### Co-authors

Stephen Davis (RMIT University) Prof. Maria Diuk-Wasser (Columbia University)

### Presentation Materials

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