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

Abstract

Tick-borne zoonotic diseases pose an escalating global health threat, yet existing mathematical models often oversimplify the complex multi-host, multi-vector transmission dynamics, particularly neglecting non-viraemic (co-feeding) transmission and differential immunity mechanisms across species. We developed a novel compartmental model explicitly incorporating five transmission pathways: tick-to-human, animal-to-animal, animal-to-tick, tick-to-animal, and non-viraemic tick-to-tick transmission. The model uniquely captures transovarial transmission in ticks, species-specific immunity (permanent in animals, temporary in humans), and disease-induced mortality. Understanding how these multiple pathways interact is crucial for designing effective integrated control strategies targeting both vector and reservoir populations, particularly in regions experiencing ecological changes that favor tick proliferation. We derived the basic reproduction number R₀ and proved its positivity, showing that animal-to-animal transmission and non-viraemic tick transmission are the dominant drivers of disease persistence (R₀ > 1). Global stability analysis confirmed that the disease-free equilibrium is globally asymptotically stable when R₀ < 1. Sensitivity analysis revealed that reducing animal treatment time and limiting inter-animal contact have the greatest impact on reducing R₀. Our results demonstrate that tick control alone is insufficient; integrated strategies combining animal vaccination/treatment, movement restrictions, and tick population management are essential. The framework is adaptable to various tick-borne pathogens (Lyme disease, tick-borne encephalitis, Crimean-Congo hemorrhagic fever) and provides quantitative guidance for resource allocation in disease control programs.