Stability analysis of a modified general SEIR model with harmonic mean type of incidence rate

A generalized SEIR epidemic dynamical model is developed to study the transmission of infectious diseases. The model includes a harmonic incidence rate. The model has been built using strong mathematical conclusions regarding stability. The model includes three equilibrium points: a disease free equ...

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Main Authors: Sant Ram Chawla, Saeed Ahmad, Wedad Albalawi, Asaf Khan, Ismail Shah, Mohamed R. Eid
Format: Article
Language:English
Published: Elsevier 2025-08-01
Series:Alexandria Engineering Journal
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S111001682500821X
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author Sant Ram Chawla
Saeed Ahmad
Wedad Albalawi
Asaf Khan
Ismail Shah
Mohamed R. Eid
author_facet Sant Ram Chawla
Saeed Ahmad
Wedad Albalawi
Asaf Khan
Ismail Shah
Mohamed R. Eid
author_sort Sant Ram Chawla
collection DOAJ
description A generalized SEIR epidemic dynamical model is developed to study the transmission of infectious diseases. The model includes a harmonic incidence rate. The model has been built using strong mathematical conclusions regarding stability. The model includes three equilibrium points: a disease free equilibrium E0, an infection-free equilibrium E1 and an endemic equilibrium E2. Using the direct technique of Lyapunov and LaSalle’s invariance principle, we demonstrate that E0 is globally asymptotically stable if R0<1, and globally asymptotically unstable if R0>1, under specific model parameter conditions. The present study involves sensitivity analysis, as the issue provided demonstrates bifurcation. The maximal principle of Pontryagin is utilized to select the best control methods for the specified model. In conclusion, the analytical results of this study are supported and verified by numerical simulations conducted under settings that are physiologically relevant.
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publishDate 2025-08-01
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series Alexandria Engineering Journal
spelling doaj-art-0aef84f4d2754724b6fd7e07e2294afa2025-08-22T04:55:44ZengElsevierAlexandria Engineering Journal1110-01682025-08-011271183119210.1016/j.aej.2025.07.006Stability analysis of a modified general SEIR model with harmonic mean type of incidence rateSant Ram Chawla0Saeed Ahmad1Wedad Albalawi2Asaf Khan3Ismail Shah4Mohamed R. Eid5Department of Mathematics University of Malakand Chakdara Dir (L) Pakhtunkhwa, PakistanDepartment of Mathematics University of Malakand Chakdara Dir (L) Pakhtunkhwa, Pakistan; Corresponding author.Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics and Statistics University of Swat Pakhtunkhwa, PakistanDepartment of Mathematics University of Malakand Chakdara Dir (L) Pakhtunkhwa, PakistanCenter for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi ArabiaA generalized SEIR epidemic dynamical model is developed to study the transmission of infectious diseases. The model includes a harmonic incidence rate. The model has been built using strong mathematical conclusions regarding stability. The model includes three equilibrium points: a disease free equilibrium E0, an infection-free equilibrium E1 and an endemic equilibrium E2. Using the direct technique of Lyapunov and LaSalle’s invariance principle, we demonstrate that E0 is globally asymptotically stable if R0<1, and globally asymptotically unstable if R0>1, under specific model parameter conditions. The present study involves sensitivity analysis, as the issue provided demonstrates bifurcation. The maximal principle of Pontryagin is utilized to select the best control methods for the specified model. In conclusion, the analytical results of this study are supported and verified by numerical simulations conducted under settings that are physiologically relevant.http://www.sciencedirect.com/science/article/pii/S111001682500821XBasic reproduction numberStability analysisOptimal controlSensitivity analysisNumerical simulations
spellingShingle Sant Ram Chawla
Saeed Ahmad
Wedad Albalawi
Asaf Khan
Ismail Shah
Mohamed R. Eid
Stability analysis of a modified general SEIR model with harmonic mean type of incidence rate
Alexandria Engineering Journal
Basic reproduction number
Stability analysis
Optimal control
Sensitivity analysis
Numerical simulations
title Stability analysis of a modified general SEIR model with harmonic mean type of incidence rate
title_full Stability analysis of a modified general SEIR model with harmonic mean type of incidence rate
title_fullStr Stability analysis of a modified general SEIR model with harmonic mean type of incidence rate
title_full_unstemmed Stability analysis of a modified general SEIR model with harmonic mean type of incidence rate
title_short Stability analysis of a modified general SEIR model with harmonic mean type of incidence rate
title_sort stability analysis of a modified general seir model with harmonic mean type of incidence rate
topic Basic reproduction number
Stability analysis
Optimal control
Sensitivity analysis
Numerical simulations
url http://www.sciencedirect.com/science/article/pii/S111001682500821X
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