Modeling Tick-Borne Zoonoses with Multi-Host and Multi-Vector Transmission Dynamics

Tick-borne zoonotic diseases pose a growing threat to public health, especially in regions where ecological and climatic conditions favor tick proliferation and pathogen persistence. This study presents a novel compartmental model that captures the complex interactions between humans, animals, and tick vectors in the transmission of a tick-borne disease. The model incorporates five distinct transmission pathways: tick-to-human, animal-to-animal, animal-to-tick, tick-to-animal, and non-viraemic (co-feeding) transmission among ticks. Additional biological features include transovarial transmission in ticks and permanent immunity in recovered animal hosts, while human hosts can be re-infected and infected ticks are assumed to remain infectious for their short lifespan. We derive analytical expressions for the basic reproduction number ($R_0$) and determine conditions for disease persistence and eradication. Through scenario-based simulations, we explore the influence of ecological and behavioral parameters—such as host interactions and contact behavior—on disease spread. Our results underscore the importance of targeting both vector and host populations in integrated control strategies and provide a flexible framework adaptable to a variety of tick-borne disease systems.