Lyme disease is the most common vector-borne disease in the United States impacting the Northeast and Midwest at the highest rates. Recently, it has become established in southeastern and south-central regions of Canada. In these regions, Lyme disease is caused by Borrelia burgdorferi, which is transmitted to humans by an infected Ixodes scapularis tick. Understanding the parasite-host interaction is critical as the white-footed mouse is one of the most competent reservoir for B. burgdorferi. The cycle of infection is driven by tick larvae feeding on infected mice that molt into infected nymphs and then transmit the disease to another susceptible host such as mice or humans. Lyme disease in humans is generally caused by the bite of an infected nymph. The main aim of this investigation is to study how diapause delays and demographic and seasonal variability in tick births, deaths, and feedings impact the infection dynamics of the tick-mouse cycle. We model tick-mouse dynamics with fixed diapause delays and more realistic Erlang distributed delays through delay and ordinary differential equations (ODEs). To account for demographic and seasonal variability, the ODEs are generalized to a continuous-time Markov chain (CTMC). The basic reproduction number and parameter sensitivity analysis are computed for the ODEs. The CTMC is used to investigate the probability of Lyme disease emergence when ticks and mice are introduced, a few of which are infected. The probability of disease emergence is highly dependent on the time and the infected species introduced. Infected mice introduced during the summer season result in the highest probability of disease emergence.
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Modeling the Effects of Ehrlichia chaffeensis and Movement on Dogs
Ehrlichia chaffeensisis a tick‐borne infectious disease transmitted byAmblyomma americanumtick. This infectious disease was discovered in the 1970s when military dogs were returning from the Vietnam War. The disease was found to be extremely severe in German Shepherds, Doberman Pinschers, Belgium Malinois, and Siberian Huskies. In this study, we developed a mathematical model for dogs and ticks infected withEhrlichia chaffeensiswith the aim of understanding the impact of movement on dogs as they move from one location to another. This could be a dog taken on a walk in an urban area or on a hike in the mountains. We carried out a global sensitivity analysis with and without movement between three locations using as response functions the sum of acutely and chronically infected ticks and the sum of infected ticks in all life stages. The parameters with the most significant impact on the response functions are dogs disease progression rate, dogs chronic infection progression rate, dogs recovery rate, dogs natural death rate, acutely and chronically infected dogs disease‐induced death rate, dogs birth rate, eggs maturation rates, tick biting rate, dogs and ticks transmission probabilities, ticks death rate, and the location carrying capacity. Our simulation results show that infection in dogs and ticks are localized in the absence of movement and spreads between locations with highest infection in locations with the highest rate movement. Also, the effect of the control measures which reduces infection trickles to other locations (trickling effect) when controls are implemented in a single location. The trickling effect is strongest when control is implemented in a location with the highest movement rate into it.
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- Award ID(s):
- 1920946
- PAR ID:
- 10526112
- Editor(s):
- Cai, Ning
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Complexity
- Volume:
- 2024
- Issue:
- 1
- ISSN:
- 1076-2787
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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