Optimal control analysis of vector-host model with saturated treatment

Area of Science:

• Epidemiology
• Mathematical Biology
• Public Health

Background:

• Vector-borne diseases pose a significant global health threat, causing millions of deaths annually.
• Developing countries often face limited medical resources during outbreaks, exacerbating disease spread.
• Understanding disease transmission dynamics is crucial for effective control.

Purpose of the Study:

• To develop and analyze a mathematical model for vector-borne disease transmission dynamics.
• To investigate the impact of nonlinear incidence and saturated treatment functions (Holling type II).
• To explore disease eradication strategies through optimal control.

Main Methods:

• Formulation of a mathematical epidemic model with nonlinear incidence and treatment.
• Analysis of model solutions for positivity and boundedness.
• Stability analysis of equilibria using Lyapunov functions and central manifold theory.
• Global sensitivity analysis using Latin Hypercube sampling and partial rank correlation coefficient.
• Optimal control problem formulation and investigation of necessary optimality conditions.

Main Results:

• The basic reproduction number ($$) and model equilibria stability were determined.
• The existence of backward bifurcation was investigated.
• Global sensitivity analysis identified key parameters influencing disease dynamics.
• Four distinct control strategies were simulated to assess their effectiveness in disease minimization.

Conclusions:

• The study provides a robust mathematical framework for understanding vector-borne disease transmission.
• Optimal control strategies demonstrate the potential for disease eradication in communities.
• The findings underscore the importance of targeted interventions, especially in resource-limited regions.