Delay-driven dynamics in a host-vector model of canine Chagas disease

Area of Science:

• Mathematical Biology
• Epidemiology
• Parasitology

Background:

• Canine Chagas disease, caused by Trypanosoma cruzi, poses a significant One Health challenge.
• Understanding host-vector interactions is crucial for disease control.

Purpose of the Study:

• To develop and analyze a mathematical model for canine Chagas disease transmission dynamics.
• To investigate the impact of time delays and transmission parameters on disease spread.

Main Methods:

• Deterministic delay differential equation model for host-vector interactions.
• Analysis of model qualitative properties (positivity, boundedness).
• Calculation of basic reproduction number using the next-generation matrix method.
• Development and application of nonstandard finite difference (NSFD) schemes.
• Numerical simulations to validate analytical results.

Main Results:

• Model analysis confirmed biological feasibility and derived equilibrium points.
• Sensitivity analysis identified key parameters influencing disease transmission.
• Time delays were found to reduce effective transmission and alter transient dynamics.
• Transmission parameters significantly impact disease persistence and spread.
• NSFD schemes successfully preserved model qualitative properties.

Conclusions:

• The mathematical model provides valuable insights into canine Chagas disease dynamics.
• Time delays are critical factors in modulating disease transmission.
• The framework aids in exploring effective disease control strategies and long-term epidemiological behavior.