Open Access

ARTICLE

Computational Modeling of Streptococcus Suis Dynamics via Stochastic Delay Differential Equations

Umar Shafique¹, Ali Raza^2,7,*, Dumitru Baleanu³, Khadija Nasir⁴, Muhammad Naveed⁵, Abu Bakar Siddique¹, Emad Fadhal^6,*

1 Department of Mathematics, National College of Business Administration and Economics, Lahore, 54000, Pakistan
2 Center for Research in Mathematics and Applications (CIMA), Institute for Advanced Studies and Research (IIFA), University of Évora, Rua Romão Ramalho, 59, Évora, 7000-671, Portugal
3 Department of Computer Science and Mathematics, Lebanese American University, Beirut, 1102-2081, Lebanon
4 Department of Zoology, University of Sialkot, Sialkot, 51040, Pakistan
5 Department of Mathematics, Air University, Islamabad, 44000, Pakistan
6 Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa, 31982, Saudi Arabia
7 Department of Physical Sciences, The University of Chenab, Gujrat, 50700, Pakistan

* Corresponding Authors: Ali Raza. Email: ,; Emad Fadhal. Email:

(This article belongs to the Special Issue: Advances in Mathematical Modeling: Numerical Approaches and Simulation for Computational Biology)

Computer Modeling in Engineering & Sciences 2025, 143(1), 449-476. https://doi.org/10.32604/cmes.2025.061635

Received 29 November 2024; Accepted 05 February 2025; Issue published 11 April 2025

Abstract

Streptococcus suis (S. suis) is a major disease impacting pig farming globally. It can also be transferred to humans by eating raw pork. A comprehensive study was recently carried out to determine the indices through multiple geographic regions in China. Methods: The well-posed theorems were employed to conduct a thorough analysis of the model’s feasible features, including positivity, boundedness equilibria, reproduction number, and parameter sensitivity. Stochastic Euler, Runge Kutta, and Euler Maruyama are some of the numerical techniques used to replicate the behavior of the streptococcus suis infection in the pig population. However, the dynamic qualities of the suggested model cannot be restored using these techniques. Results: For the stochastic delay differential equations of the model, the non-standard finite difference approach in the sense of stochasticity is developed to avoid several problems such as negativity, unboundedness, inconsistency, and instability of the findings. Results from traditional stochastic methods either converge conditionally or diverge over time. The stochastic non-negative step size convergence nonstandard finite difference (NSFD) method unconditionally converges to the model’s true states. Conclusions: This study improves our understanding of the dynamics of streptococcus suis infection using versions of stochastic with delay approaches and opens up new avenues for the study of cognitive processes and neuronal analysis. The plotted interaction behaviour and new solution comparison profiles.

---

Keywords

---