Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

Karim Khan,Amir Khan,Abdullahi Yusuf,Rahat Zarin,Arif Ullah,Mohammed Al-Shomrani

doi:10.1186/s13662-021-03249-4

Abstract

In this paper, we discuss the Anthroponotic Cutaneous Leishmania transmission. In addition, we develop a mathematical model for the Anthroponotic Cutaneous Leishmania transmission and consider its qualitative behavior. We derive the threshold number R_{0} of the model using the next generation method. In the disease-free case, we carry out the local and global stability under the condition R_{0}<1. Moreover, we derive the global stability at the disease-free equilibrium point by utilizing the Castillo-Chavez method. On the other hand, at the endemic equilibrium point, we show the local and global stability to be held under specific conditions and R_{0}>1. We also establish the global stability at the endemic equilibrium point with the help of a geometrical approach, which is a generalization of Lyapunov theory, by using a second additive compound matrix. Finally, we take into account the sensitivity analysis of the threshold number with other parameters. We also discuss several graphs of important parameters.

Highlights

Leishmaniasis is the sixth most common disease affecting public health worldwide
Different lab tests are performed to diagnose this parasite; for example, blood test for antibodies against the parasite, urine tests, and polymerase chain reaction (PCR) test can identify parasite based on its genetic fingerprint, and smear test identifies the parasite through a microscope
Treatment protocols: we present a number of cases of Cutaneous Leishmaniasis (CL) lesions at different sites of the body treated with Photodynamic therapy (PDT) from Pakistan

Summary

Introduction

Leishmaniasis is the sixth most common disease affecting public health worldwide. It is a vector borne disease transmitted among mammalian hosts by the female sand fly. Most common animals carrying the Leishmania parasite are rodents, dogs, cattles, and foxes, this parasite primarily affecting the skin. The sand flies are the main transmitter of these parasites. The habitat of these flies enjoys a wide range, from desert to tropical rain forest. These and several hosts in which dogs, chickens, humans, mammals, livestock, and vertebrates are considered to be

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