TY  - JOUR
AU  - Jiao, Hui
AU  - Dai, Shiyuan
AU  - Jiao, Jianjun
PY  - 2026
DA  - 2026/09/22
TI  - Dynamics of An SIR Model with Isolation and Pulse Vaccinated Susceptible Population for Delay Acquiring Immunity
JO  - Journal of Mathematics and Interdisciplinary Applications
T2  - Journal of Mathematics and Interdisciplinary Applications
JF  - Journal of Mathematics and Interdisciplinary Applications
VL  - 2
IS  - 3
SP  - 229
EP  - 237
DO  - 10.62762/JMIA.2026.436736
UR  - https://www.icck.org/article/abs/JMIA.2026.436736
KW  - SIR model
KW  - isolation
KW  - pulse vaccination
KW  - delay in acquiring immunity
KW  - infection-free periodic solution
KW  - endemic disease
AB  - Vaccination is one of the most cost-effective and simplest interventions for protecting against infectious-disease epidemics. The COVID-19 (coronavirus disease 2019) outbreak in China demonstrated that physical protection and social isolation are critical to controlling an epidemic in the absence of vaccines or antiviral drugs. Considering isolation and pulse vaccination of the susceptible population subject to a delay in acquiring immunity, we propose a susceptible-infectious-recovered (SIR) model incorporating these features. Using the theory of impulsive differential equations and comparison theorems, we prove that the infection-free periodic solution $(\widetilde{S(t)},0)$ of system $(3.1)$ is globally asymptotically stable if $H0$. The expression of $H$ and the numerical simulations indicate that isolation and the delay in acquiring immunity of the vaccinated susceptible population play important roles in achieving the infection-free state, and that the maximum enrolling amount from the exterior region also affects disease elimination.
SN  - 3070-393X
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Jiao2026Dynamics,
  author = {Hui Jiao and Shiyuan Dai and Jianjun Jiao},
  title = {Dynamics of An SIR Model with Isolation and Pulse Vaccinated Susceptible Population for Delay Acquiring Immunity},
  journal = {Journal of Mathematics and Interdisciplinary Applications},
  year = {2026},
  volume = {2},
  number = {3},
  pages = {229-237},
  doi = {10.62762/JMIA.2026.436736},
  url = {https://www.icck.org/article/abs/JMIA.2026.436736},
  abstract = {Vaccination is one of the most cost-effective and simplest interventions for protecting against infectious-disease epidemics. The COVID-19 (coronavirus disease 2019) outbreak in China demonstrated that physical protection and social isolation are critical to controlling an epidemic in the absence of vaccines or antiviral drugs. Considering isolation and pulse vaccination of the susceptible population subject to a delay in acquiring immunity, we propose a susceptible-infectious-recovered (SIR) model incorporating these features. Using the theory of impulsive differential equations and comparison theorems, we prove that the infection-free periodic solution \$(\widetilde{S(t)},0)\$ of system \$(3.1)\$ is globally asymptotically stable if \$H0\$. The expression of \$H\$ and the numerical simulations indicate that isolation and the delay in acquiring immunity of the vaccinated susceptible population play important roles in achieving the infection-free state, and that the maximum enrolling amount from the exterior region also affects disease elimination.},
  keywords = {SIR model, isolation, pulse vaccination, delay in acquiring immunity, infection-free periodic solution, endemic disease},
  issn = {3070-393X},
  publisher = {Institute of Central Computation and Knowledge}
}