Qualitative behavior of a highly non-linear Cutaneous Leishmania epidemic model under convex incidence rate with real data

被引：23

作者：

Alqhtani M. ^{[1
]}

Saad K.M. ^{[1
]}

Zarin R. ^{[2
]}

Khan A. ^{[3
]}

Hamanah W.M. ^{[4
,5
]}

机构：

[1] Department of Mathematics, College of Sciences and Arts, Najran University, Najran

[2] Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology, Thonburi (KMUTT), Bangkok

[3] Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa

[4] Applied Research Center for Metrology, Standards, and Testing, King Fahd University of Petroleum and Minerals, Dhahran

[5] Department of Electrical Engineering, College of Engineering and Physics, King Fahd University for Petroleum and Minerals, Dhahran

来源：

Mathematical Biosciences and Engineering | 2024年 / 21卷 / 02期

关键词：

bifurcation; compound matrix; geometric approach; real data; sensitivity analysis; stability analysis;

D O I：

10.3934/mbe.2024092

中图分类号：

学科分类号：

摘要：

In the context of this investigation, we introduce an innovative mathematical model designed to elucidate the intricate dynamics underlying the transmission of Anthroponotic Cutaneous Leishmania. This model offers a comprehensive exploration of the qualitative characteristics associated with the transmission process. Employing the next-generation method, we deduce the threshold value R0 for this model. We rigorously explore both local and global stability conditions in the disease-free scenario, contingent upon R0 being less than unity. Furthermore, we elucidate the global stability at the disease-free equilibrium point by leveraging the Castillo-Chavez method. In contrast, at the endemic equilibrium point, we establish conditions for local and global stability, when R0 exceeds unity. To achieve global stability at the endemic equilibrium, we employ a geometric approach, a Lyapunov theory extension, incorporating a secondary additive compound matrix. Additionally, we conduct sensitivity analysis to assess the impact of various parameters on the threshold number. Employing center manifold theory, we delve into bifurcation analysis. Estimation of parameter values is carried out using least squares curve fitting techniques. Finally, we present a comprehensive discussion with graphical representation of key parameters in the concluding section of the paper. © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License.

引用

页码：2084 / 2120

页数：36

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