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This research employs a modified version of the Lotka-Volterra non-linear first-order ordinary differential equations to model and analyze the parasitic impact of ticks on dogs. The analysis reveals that fluctuations in pesticide effects significantly influence tick populations and the size of the canine host. The study also uncovers that alterations in the size of the interacting species can lead to both stable and unstable states. Interestingly, in a pesticide-free environment, a decline in the inter-competition coefficient catalyzes an increase in the sizes of both interacting species. This increase, although marginal for the tick population, contributes to overall system stability. The findings underscore the utility of the Lotka-Volterra non-linear first-order ordinary differential equations in modeling the parasitic effect of ticks on dogs. To protect pets, particularly dogs, from the harmful effects of tick infestation, this study recommends the appropriate and regular application of disinfectants. [ABSTRACT FROM AUTHOR]