Analysis of the dynamics and optimal control of cutaneous Lieshmania during human immigration

Articles in Press

Document Type : Research Article

Authors

• Hamza Toufga
• Ayoub Sakkoum
• Lahbib Benahmadi
• Mustapha Lhous

Fundamental and Applied Mathematics Laboratory (FAML), Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, Morocco.

10.22067/ijnao.2024.88709.1466

Abstract

Lieshmania is an infectious disease that is difficult to control and has an impact on morbidity and mortality around the world. This study investigates the dynamics of cutaneous lieshmania and optimal control measures, particularly in regards to human immigration. Applying a mathematical model to evaluate the dynamics of human immigration and sand flies population. The human population is classified into four compartments: susceptible, exposed, infectious, and recovered. The sand fly population is divided into three categories: susceptible, exposed, and infectious. The mathematical analysis involves positivity, existence and the uniqueness of the solution. We analyzed the global stability of the system around the endemic equilibrium point by contracting the Lyapunov function. Optimal control measures are used to reduce the number of infected and exposed individuals among humans, sand flies, and migrants. These techniques are described using Pontryagin's Maximum Principle to derive necessary conditions for optimal control. The numerical simulations confirm the theoretical results by showing that following these controls effectively reduces the spread of the disease, and immigration has a major impact on the spread of human-borne lieshmania.

Keywords

• Lieshmania
• mathematical model
• immigration
• stability
• optimal control

Main Subjects

• Optimal Control

---