Stochastic delay derivatives of Newcastle disease application in epidemic model: Stability analysis and approximation
5 affiliations
- 1Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
- 2Department of Mathematics, Firat University, Elazığ, Türkiye
- 3IT4Innovations, VSB-Technical University of Ostrava, Ostrava, Czech Republic
- 4Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan
- 5Mathematical Science Department, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
Abstract
The illicit trade in wildlife for pet purposes poses a direct risk to animal populations through overharvesting, but it also serves as an indirect conduit for the spread of contagious diseases. The present study assessed the effects of the hypothetical release of captured, infected individuals of Newcastle disease into the natural population of the white-winged parakeet, the most trafficked psittacine species in Peru. This study analysed the computational dynamical analysis of the stochastic susceptible-exposed-infected-recovered model of Newcastle disease. We take two approaches to stochastic modelling: transition probabilities and the perturbation method. To investigate dynamical features such as positivity, boundedness, consistency, and stability, we introduced a stochastic non-standard finite-difference (SNSFD) scheme. Conventional numerical approaches such as Euler-Maruyama, stochastic Euler, and stochastic Runge–Kutta of order four were applied, but they failed to preserve the system’s essential dynamical properties. Consequently, we formulated the SNSFD method to address this limitation. To support the proposed method, we presented several theorems that demonstrate it satisfies all dynamical properties of the model. In the end, we presented several simulations to compare the proposed method’s efficiency to that of an existing method.
Related
- Stochastic evolutionary dynamics in structured populations: Network degree governs evolutionary stability
- Diagnosing parameter unidentifiability in stochastic dynamics with an application to flocking models
- Oncolytic Newcastle disease virus promotes tumor cell apoptosis through SUMO-1-dependent PRKN-mediated degradation of c-Myc
- Recombinant GI-19 infectious bronchitis virus induction of humoral immunosuppression with reduced HI antibody response following Newcastle disease virus vaccination and bursal cell apoptosis
- Assessment of TLR3-TRIF-NF-κB Innate Immune Signaling Pathway Induced by Newcastle Disease Virus and Construction of TLR3-Deficient BHK-21 Cells.
BibTeX
@article{shahid2026stochastic,
title = {{Stochastic delay derivatives of Newcastle disease application in epidemic model: Stability analysis and approximation}},
author = {Naveed Shahid and Ali Raza and Marek Lampart and Sana Iqbal and Nauman Ahmed and Eman Ghareeb Rezk},
journal = {PLOS One},
year = {2026},
month = sep,
doi = {10.1371/journal.pone.0357918},
url = {https://doi.org/10.1371/journal.pone.0357918},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Stochastic delay derivatives of Newcastle disease application in epidemic model: Stability analysis and approximation
AU - Naveed Shahid
AU - Ali Raza
AU - Marek Lampart
AU - Sana Iqbal
AU - Nauman Ahmed
AU - Eman Ghareeb Rezk
PY - 2026
DA - 2026/09/17
JO - PLOS One
DO - 10.1371/journal.pone.0357918
UR - https://doi.org/10.1371/journal.pone.0357918
AB - The illicit trade in wildlife for pet purposes poses a direct risk to animal populations through overharvesting, but it also serves as an indirect conduit for the spread of contagious diseases. The present study assessed the effects of the hypothetical release of captured, infected individuals of Newcastle disease into the natural population of the white-winged parakeet, the most trafficked psittacine species in Peru. This study analysed the computational dynamical analysis of the stochastic susceptible-exposed-infected-recovered model of Newcastle disease. We take two approaches to stochastic modelling: transition probabilities and the perturbation method. To investigate dynamical features such as positivity, boundedness, consistency, and stability, we introduced a stochastic non-standard finite-difference (SNSFD) scheme. Conventional numerical approaches such as Euler-Maruyama, stochastic Euler, and stochastic Runge–Kutta of order four were applied, but they failed to preserve the system’s essential dynamical properties. Consequently, we formulated the SNSFD method to address this limitation. To support the proposed method, we presented several theorems that demonstrate it satisfies all dynamical properties of the model. In the end, we presented several simulations to compare the proposed method’s efficiency to that of an existing method.
SN - 1932-6203
ER -