Mathematical model of Ehrlichia chaffeensis transmission dynamics in dogs

Abstract

Ehrlichia chaffeensis is a tick-borne disease transmitted by ticks to dogs. Few studies have mathematical modelled such tick-borne disease in dogs, and none have developed models that incorporate different ticks' developmental stages (discrete variable) as well as the duration of infection (continuous variable). In this study, we develop and analyze a model that considers these two structural variables using integrated semigroups theory. We address the well-posedness of the model and investigate the existence of steady states. The model exhibits a disease-free equilibrium and an endemic equilibrium. We calculate the reproduction number (${\mathcal{T}}_0$). We establish a necessary and sufficient condition for the bifurcation of an endemic equilibrium. Specifically, we demonstrate that a bifurcation, either backward or forward, can occur at ${\mathcal{T}}_0=1$, leading to the existence, or not, of an endemic equilibrium even when ${\mathcal{T}}_0<1$. Finally, numerical simulations are employed to illustrate these theoretical findings.

Keywords:

• Amblyomma americanum
• Ehrlichia chaffeensis
• age-structured model
• bifurcation analysis

MATHEMATICS SUBJECT CLASSIFICATIONs:

• 92-10
• 92D30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

FBA is supported by the National Science Foundation under the EPSCOR Track 2 grant number 1920946.