Network-level reproduction number and extinction threshold for vector-borne diseases.

Area of Science:

• Epidemiology
• Mathematical Biology
• Network Science

Background:

• The basic reproduction number (R0) is crucial for predicting epidemic spread.
• Disease extinction thresholds inform control, elimination, and mitigation strategies.
• Understanding R0 and extinction thresholds is vital for vector-borne disease management.

Purpose of the Study:

• To derive relationships between R0 in deterministic network models and extinction thresholds in stochastic models.
• To investigate the relationship between R0 and extinction thresholds using numerical simulations.
• To provide insights into disease mitigation strategies for vector-borne diseases.

Main Methods:

• Developed deterministic network-based ordinary differential equation vector-host models.
• Derived relationships between R0 and extinction thresholds under specific assumptions.
• Employed stochastic continuous-time Markov chain models for extinction threshold analysis.
• Conducted numerical simulations for malaria and Rift Valley fever transmission on heterogeneous networks.

Main Results:

• Established analytical relationships between R0 and extinction thresholds.
• Numerical simulations confirmed analytical results, suggesting general applicability.
• Observed that R0 does not monotonically correlate with the extinction threshold.
• Identified consistent trends in extinction probability for improved mitigation.

Conclusions:

• The derived relationships between R0 and extinction thresholds may hold generally.
• Findings enhance understanding of disease persistence thresholds for vector-borne diseases.
• Insights support the development of effective disease control and mitigation strategies.