Competitive exclusion in a vector-host model for the dengue fever

Area of Science:

• Epidemiology
• Mathematical Biology
• Virology

Background:

• Dengue fever is a significant vector-borne disease caused by four serotypes of the dengue virus.
• Each serotype induces host immunity, but cross-immunity to other serotypes is often partial and temporary.
• Understanding the dynamics of competing pathogen strains is crucial for disease control.

Purpose of the Study:

• To develop and analyze a mathematical model for the population dynamics of a vector-transmitted disease with two pathogen strains.
• To investigate the conditions that permit the coexistence of competing strains, using dengue fever as a case study.
• To explore epidemiological trends and the factors influencing competitive exclusion.

Main Methods:

• A system of differential equations was formulated to model the SIR (Susceptible-Infectious-Recovered) dynamics.
• The model incorporates temporary cross-immunity between two viral strains.
• Numerical simulations were employed to support analytical findings on equilibria and stability.

Main Results:

• The model demonstrates an unstable endemic equilibrium (saddle point), leading to long transient periods where both strains cocirculate.
• Conditions for the asymptotic stability of different equilibria were analyzed.
• The study identified the interplay between host superinfection and frequency-dependent contact rates as key drivers of competitive exclusion.

Conclusions:

• The mathematical model successfully reproduces epidemic dynamics observed in dengue fever.
• Temporary cross-immunity and host superinfection, coupled with frequency-dependent transmission, can lead to the long-term cocirculation of competing pathogen strains.
• The findings provide insights into the complex epidemiological dynamics of diseases like dengue and inform strategies for disease management.