Transmission Dynamics of an Infectious Disease with Vaccination and Multiple Infection Classes

Bouziane Mehdi; Harun Baldemir

doi:10.32323/ujma.1991397

Transmission Dynamics of an Infectious Disease with Vaccination and Multiple Infection Classes

Abstract

In this paper, we propose an improved SEIR epidemic model that incorporates waning vaccine-induced immunity and divides the infected population into three distinct classes. The model captures more realistic disease dynamics by accounting for waning vaccine-induced immunity among vaccinated individuals and heterogeneous infectious stages. Fundamental properties of the model, including the existence, uniqueness, positivity and boundedness of solutions, are established to ensure its mathematical and epidemiological validity.The disease-free equilibrium is derived and the vaccination reproduction number ($R_v$) is computed using the next-generation matrix approach. Conditions for the existence of an endemic equilibrium are established, and numerical simulations indicate that, for the parameter regimes considered, the disease-free equilibrium is locally asymptotically stable when $R_v<1$, while the endemic equilibrium is locally stable when $R_v>1$. Additional simulations are carried out to illustrate the effects of key epidemiological parameters.Furthermore, sensitivity analysis is performed to assess the influence of model parameters on $R_v$ and the state variables. The results highlight the dominant roles of the effective contact/transmission rates and the vaccine waning rate in shaping $R_v$. Overall, the proposed model provides a useful framework for evaluating vaccination strategies and informing public health interventions aimed at controlling infectious disease transmission.

Keywords

Epidemic model, Vaccination, Multiple infection classes, Sensitivity analysis

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations

Journal Section

Research Article

Authors

Bouziane Mehdi
0009-0009-4808-7831
Algeria

Harun Baldemir ^*
0000-0002-2599-1117
Türkiye

Early Pub Date

September 8, 2026

Publication Date

September 13, 2026

Submission Date

July 10, 2026

Acceptance Date

September 1, 2026

Published in Issue

Year 2026 Volume: 9 Number: 3

DOI

https://doi.org/10.32323/ujma.1991397

IZ

https://izlik.org/JA36JR53JY

APA

Mehdi, B., & Baldemir, H. (2026). Transmission Dynamics of an Infectious Disease with Vaccination and Multiple Infection Classes. Universal Journal of Mathematics and Applications, 9(3), 191-202. https://doi.org/10.32323/ujma.1991397

AMA

1.Mehdi B, Baldemir H. Transmission Dynamics of an Infectious Disease with Vaccination and Multiple Infection Classes. Univ. J. Math. Appl. 2026;9(3):191-202. doi:10.32323/ujma.1991397

Chicago

Mehdi, Bouziane, and Harun Baldemir. 2026. “Transmission Dynamics of an Infectious Disease With Vaccination and Multiple Infection Classes”. Universal Journal of Mathematics and Applications 9 (3): 191-202. https://doi.org/10.32323/ujma.1991397.

EndNote

Mehdi B, Baldemir H (September 1, 2026) Transmission Dynamics of an Infectious Disease with Vaccination and Multiple Infection Classes. Universal Journal of Mathematics and Applications 9 3 191–202.

IEEE

[1]B. Mehdi and H. Baldemir, “Transmission Dynamics of an Infectious Disease with Vaccination and Multiple Infection Classes”, Univ. J. Math. Appl., vol. 9, no. 3, pp. 191–202, Sept. 2026, doi: 10.32323/ujma.1991397.

ISNAD

Mehdi, Bouziane - Baldemir, Harun. “Transmission Dynamics of an Infectious Disease With Vaccination and Multiple Infection Classes”. Universal Journal of Mathematics and Applications 9/3 (September 1, 2026): 191-202. https://doi.org/10.32323/ujma.1991397.

JAMA

1.Mehdi B, Baldemir H. Transmission Dynamics of an Infectious Disease with Vaccination and Multiple Infection Classes. Univ. J. Math. Appl. 2026;9:191–202.

MLA

Mehdi, Bouziane, and Harun Baldemir. “Transmission Dynamics of an Infectious Disease With Vaccination and Multiple Infection Classes”. Universal Journal of Mathematics and Applications, vol. 9, no. 3, Sept. 2026, pp. 191-02, doi:10.32323/ujma.1991397.

Vancouver

1.Bouziane Mehdi, Harun Baldemir. Transmission Dynamics of an Infectious Disease with Vaccination and Multiple Infection Classes. Univ. J. Math. Appl. 2026 Sep. 1;9(3):191-202. doi:10.32323/ujma.1991397