An age-structured vector-borne disease model with horizontal transmission in the host

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Dynamics

Background:

• Vector-borne diseases pose significant public health challenges.
• Understanding disease transmission dynamics is crucial for control strategies.
• Infection age and horizontal transmission are key factors in disease spread.

Purpose of the Study:

• To develop and analyze a mathematical model for vector-borne diseases.
• To investigate the role of infection age and horizontal transmission.
• To establish the threshold dynamics governing disease persistence or eradication.

Main Methods:

• Utilized Lyapunov functionals for stability analysis.
• Derived the basic reproduction number (R0) as the key threshold parameter.
• Employed mathematical modeling and numerical simulations.

Main Results:

• Established a clear threshold dynamics dependent on the basic reproduction number.
• Demonstrated that if R0 < 1, the infection-free equilibrium is globally asymptotically stable.
• Showed that if R0 > 1, the infected equilibrium attracts all solutions with initial infection.

Conclusions:

• The basic reproduction number is a critical determinant of vector-borne disease outcomes.
• The model provides insights into disease control by identifying critical thresholds.
• Numerical simulations support the theoretical findings on disease dynamics.