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  3. Volume 10, Number 2, 2023
  4. An epidemic model with viral mutations and vaccine interventions

An epidemic model with viral mutations and vaccine interventions

MMC.
2023;
Volume 10, Number 2
: pp. 311–325
https://doi.org/10.23939/mmc2023.02.311
Received: August 14, 2022
Revised: January 30, 2023
Accepted: February 01, 2023

Mathematical Modeling and Computing, Vol. 10, No. 2, pp. 311–325 (2023)

Authors:
  1. Y. A. Adi
  2. N. Irsalinda
  3. A. Wiraya
  4. S. Sugiyarto
  5. Z. A. Rafsanjani
1
Department of Mathematics, Faculty of Applied Science and Technology, Ahmad Dahlan University, Yogyakarta, Indonesia
2
Department of Mathematics, Faculty of Applied Science and Technology, Ahmad Dahlan University, Yogyakarta, Indonesia
3
Department of Mathematics Educations, Faculty of Teacher Training and Education, Sebelas Maret University, Surakarta, Indonesia
4
Department of Mathematics, Faculty of Applied Science and Technology, Ahmad Dahlan University, Yogyakarta, Indonesia
5
Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University, Semarang, Indonesia

In this paper, we introduce a two-strain SIR epidemic model with viral mutation and vaccine administration.  We discuss and analyze the existence and stability of equilibrium points.  This model has three types of equilibrium points, namely disease-free equilibrium, dominance equilibrium point of strain two, and coexistence endemic equilibrium point.  The local stability of the dominance equilibrium point of strain two and coexistence endemic equilibrium point are verified by using the Routh--Hurwitz criteria, while for the global stability of the dominance equilibrium point of strain two, we used a suitable Lyapunov function.  We also carried out the bifurcation analysis using the application of center manifold theory, and we obtained that the system near the disease-free equilibrium point always has supercritical bifurcation. Finally, the numerical simulations are provided to validate the theoretical results.  Continuation of the supercritical bifurcation point results in two Hopf bifurcations indicating a local birth of chaos and quasi-periodicity.

epidemic model
virus mutation
vaccination
stability analysis
bifurcation
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