Modeling the spread of Leishmaniasis disease via delayed analysis

Abstract

Leishmaniasis is a group of contagious diseases having high surveillance among dogs. According to World Health Organization (WHO), ninety-two territories were infected around the world in 2018. One billion dogs live in areas endemic for Leishmaniasis and are at risk of infection. Almost one million cases are reported annually. The dog's population is categorized into five classes like susceptible (S), latent (L), infectious (I), uninfected (R), and infected (Q). The Leishmaniasis delayed model is developed to analyze and control its spread. Equilibria, positivity, boundedness, reproduction number, and parameter sensitivity are the model's essential features. The stability of the model is investigated in a local and global sense with the help of the Routh Hurwitz criterion and Lyapunov theory. In the end, simulations are presented to verify the theoretical analysis of the delayed model.

Keywords

• Leishmaniasis disease
• Delayed model
• Stability analysis
• Computer results