Preliminary analysis of an agent-based model for a tick-borne disease
Holly Gaff
Mathematical Biosciences & Engineering 2011, 8(2): 463-473 doi: 10.3934/mbe.2011.8.463
Ticks have a unique life history including a distinct set of life stages and a single blood meal per life stage. This makes tick-host interactions more complex from a mathematical perspective. In addition, any model of these interactions must involve a significant degree of stochasticity on the individual tick level. In an attempt to quantify these relationships, I have developed an individual-based model of the interactions between ticks and their hosts as well as the transmission of tick-borne disease between the two populations. The results from this model are compared with those from previously published differential equation based population models. The findings show that the agent-based model produces significantly lower prevalence of disease in both the ticks and their hosts than what is predicted by a similar differential equation model.
keywords: Agent-based model tick-borne disease.
Identifying requirements for the invasion of a tick species and tick-borne pathogen through TICKSIM
Holly Gaff Robyn Nadolny
Mathematical Biosciences & Engineering 2013, 10(3): 625-635 doi: 10.3934/mbe.2013.10.625
Ticks and tick-borne diseases have been on the move throughout the United State over the past twenty years. We use an agent-based model, TICKSIM, to identify the key parameters that determine the success of invasion of the tick and if that is successful, the succees of the tick-borne pathogen. We find that if an area has competent hosts, an initial population of ten ticks is predicted to always establish a new population. The establishment of the tick-borne pathogen depends on three parameters: the initial prevalence in the ten founding ticks, the probability that a tick infects the longer-lived hosts and the probability that a tick infects the shorter-lived hosts. These results indicate that the transmission rates to hosts in the newly established area can be used to predict the potential risk of disease to humans.
keywords: tick-borne disease. Agent-based model
Optimal control applied to vaccination and treatment strategies for various epidemiological models
Holly Gaff Elsa Schaefer
Mathematical Biosciences & Engineering 2009, 6(3): 469-492 doi: 10.3934/mbe.2009.6.469
Mathematical models provide a powerful tool for investigating the dynamics and control of infectious diseases, but quantifying the underlying epidemic structure can be challenging especially for new and under-studied diseases. Variations of standard SIR, SIRS, and SEIR epidemiological models are considered to determine the sensitivity of these models to various parameter values that may not be fully known when the models are used to investigate emerging diseases. Optimal control theory is applied to suggest the most effective mitigation strategy to minimize the number of individuals who become infected in the course of an infection while efficiently balancing vaccination and treatment applied to the models with various cost scenarios. The optimal control simulations suggest that regardless of the particular epidemiological structure and of the comparative cost of mitigation strategies, vaccination, if available, would be a crucial piece of any intervention plan.
keywords: vaccination. SIR epidemic SEIR SIRS optimal control

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