https://doi.org/10.1140/epjp/s13360-026-07561-4
Regular Article
A Mathematical model for the co-transmission dynamics of lyme disease and babesiosis with awareness-driven behavioral responses
1
Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, 11942, Al-Kharj, Saudi Arabia
2
Department of Mathematics, College of Natural and Computational Sciences, Debre Berhan University, Debre Berhan, Ethiopia
3
Department of Computer Science, College of Computer Engineering and Sciences, Prince Sattam bin Abdulaziz University, 11942, Al-Kharj, Saudi Arabia
4
Nanoelectronics Integrated Systems Center, Nile University, 12588, Giza, Egypt
5
Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura University, 35516, Mansoura, Egypt
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
24
January
2026
Accepted:
10
March
2026
Published online:
12
April
2026
Abstract
The escalating public health burden of tick-borne diseases, particularly the frequent co-occurrence of Lyme disease and babesiosis, demands modeling frameworks that capture the complex interplay between pathogen transmission, ecological dynamics, and human behavioral responses. This study develops and rigorously analyzes a novel multi-host compartmental model that integrates, for the first time, sequential co-infection dynamics in humans, reservoir hosts, and tick vectors with awareness-driven behavioral feedback mechanisms. The model explicitly represents the bidirectional facilitation between pathogens, wherein infection with one agent expands susceptibility to the other, generating nonlinear transmission pathways absent in single-pathogen frameworks. Through comprehensive qualitative analysis, we establish solution positivity and boundedness, derive the basic reproduction number, prove local and global stability conditions for the disease-free equilibrium, and identify parameter regimes supporting backward bifurcation revealing that co-infection can lower the ecological threshold for pathogen persistence. To overcome the challenges posed by the resulting high-dimensional strongly nonlinear system, we implement a Chebyshev integral collocation method with domain decomposition and fixed-point iteration, achieving spectral accuracy with errors of order 
–
while reducing computational costs by an order of magnitude compared to conventional solvers. Sensitivity analysis identifies tick mortality as the dominant control parameter, with awareness strength and transmission rates playing secondary but significant roles. Numerical simulations demonstrate that public awareness campaigns substantially reduce both single and co-infected prevalence, providing quantitative evidence that behavioral interventions, when coupled with vector control, can drive disease elimination even in endemic settings. This work establishes an integrated analytical-numerical foundation for understanding multi-pathogen tick-borne diseases and directly informs evidence-based strategies aligned with Sustainable Development Goal 3.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
