An optimal control problem for carrier dependent diseases

Area of Science:

• Mathematical modeling
• Epidemiology
• Public health

Background:

• Houseflies act as disease vectors, particularly in developing countries.
• Disease spread is exacerbated by poor sanitation practices and economic limitations.
• Lack of public awareness contributes to the prevalence of vector-borne diseases.

Purpose of the Study:

• To develop a mathematical model for understanding disease dynamics transmitted by houseflies.
• To analyze the logistic growth of housefly populations in relation to disease spread.
• To formulate and analyze an optimization problem for controlling housefly density and disease transmission.

Main Methods:

• A mathematical model incorporating logistic housefly growth was formulated.
• The model assumes houseflies transmit bacteria from the environment to human food sources.
• An optimization problem was developed to reduce housefly populations and human infections.
• Numerical simulations were conducted to validate analytical findings.

Main Results:

• The study provides insights into the dynamics of housefly-mediated disease transmission.
• Analytical and numerical results support the proposed control strategies.
• The optimization approach identifies potential interventions to mitigate disease spread.

Conclusions:

• Mathematical modeling is a valuable tool for understanding and controlling vector-borne diseases.
• Effective disease control requires addressing both vector population dynamics and human behavior.
• Integrated strategies targeting sanitation, awareness, and vector control are crucial for public health in affected regions.