Optimal control of a tick population with a view to control of Rocky Mountain Spotted Fever

Maeve L. McCarthy; Dorothy I. Wallace; Maeve L. McCarthy; Dorothy I. Wallace

doi:10.3934/mbe.2023837

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 18916-18938. doi: 10.3934/mbe.2023837

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Optimal control of a tick population with a view to control of Rocky Mountain Spotted Fever

Maeve L. McCarthy ^{1
,
,},
Dorothy I. Wallace ²

1.
Department of Mathematics & Statistics, Murray State University, 203A Industry & Technology, Murray KY 42071, USA
2.
Department of Mathematics, Dartmouth College, 27 N. Main Street, 6188 Kemeny Hall, Hanover, NH 03755-3551, USA

Received: 24 July 2023 Revised: 13 September 2023 Accepted: 21 September 2023 Published: 10 October 2023

In some regions of the Americas, domestic dogs are the host for the tick vector Rhipicephalus sanguineus, and spread the tick-borne pathogen Rickettsia rickettsii, which causes Rocky Mountain Spotted Fever (RMSF) in humans. Interventions are carried out against the vector via dog collars and acaricidal wall treatments. This paper investigates the optimal control of acaricidal wall treatments, using a prior model for populations and disease transmission developed for this particular vector, host, and pathogen. It is modified with a death term during questing stages reflecting the cost of control and level of coverage. In the presence of the control, the percentage of dogs and ticks infected with Ri. rickettsii decreases in a short period and remains suppressed for a longer period, including after treatment is discontinued. Risk of RMSF infection declines by 90% during this time. In the absence of re-application, infected tick and dog populations rebound, indicating the eventual need for repeated treatment.
- Rocky Mountain Spotted Fever,
- Rhipicephalus sanguineus,
- Rickettsia rickettsii,
- tick-borne disease,
- optimal control,
- insecticidal wall treatment,
Citation: Maeve L. McCarthy, Dorothy I. Wallace. Optimal control of a tick population with a view to control of Rocky Mountain Spotted Fever[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18916-18938. doi: 10.3934/mbe.2023837

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Abstract

In some regions of the Americas, domestic dogs are the host for the tick vector Rhipicephalus sanguineus, and spread the tick-borne pathogen Rickettsia rickettsii, which causes Rocky Mountain Spotted Fever (RMSF) in humans. Interventions are carried out against the vector via dog collars and acaricidal wall treatments. This paper investigates the optimal control of acaricidal wall treatments, using a prior model for populations and disease transmission developed for this particular vector, host, and pathogen. It is modified with a death term during questing stages reflecting the cost of control and level of coverage. In the presence of the control, the percentage of dogs and ticks infected with Ri. rickettsii decreases in a short period and remains suppressed for a longer period, including after treatment is discontinued. Risk of RMSF infection declines by 90% during this time. In the absence of re-application, infected tick and dog populations rebound, indicating the eventual need for repeated treatment.

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