Alsulami Amer, Shahid Naveed, Ahmed Nauman, Almalahi Mohammed, Mustafa Alaa, Aldwoah Khaled
Department of Mathematics, Turabah University College, Taif University, Taif 21944, Saudi Arabia.
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
PLoS One. 2025 Jun 10;20(6):e0323975. doi: 10.1371/journal.pone.0323975. eCollection 2025.
This study aims to investigate and analyze the dynamics of diarrhea infectious disease model. For this purpose, a classical diarrhea disease model is converted into the diffusive diarrhea epidemic model by including the diffusion terms in every compartment of the system. Basic assumptions of the proposed model are described for a vivid understanding of the model's behavior. In addition, the pros and cons of the proposed model for short and long terms behavior of the diffusive system are presented. The system has two steady states, namely the disease-free equilibrium and endemic equilibrium points. The system is analyzed, analytically by ensuring the positivity, boundedness and local, and global stability at both the steady states. Moreover, the implicit nonstandard finite difference scheme is designed to extract the numerical solutions of the diffusive epidemic model. To ensure the reliability and efficacy of the numerical scheme, the positivity, consistency and both linear and nonlinear stabilities are presented by establishing some standard results. Simulated graphs are sketched to study the nonlinear behavior of the disease dynamics. All the graphs depict the positive, bounded and convergent behavior of the projected numerical scheme. Also, the numerical graphs reflect the role of the basic reproductive number, R0, in attaining the steady state. The article is closed by providing productive outcomes of the study.
本研究旨在调查和分析腹泻传染病模型的动态变化。为此，通过在系统的每个隔室中纳入扩散项，将经典的腹泻疾病模型转化为扩散性腹泻流行模型。为了清晰理解该模型的行为，阐述了所提模型的基本假设。此外，还介绍了所提模型对于扩散系统短期和长期行为的优缺点。该系统有两个稳态，即无病平衡点和地方病平衡点。通过确保在两个稳态下的正性、有界性以及局部和全局稳定性，对该系统进行了分析。此外，设计了隐式非标准有限差分格式来求解扩散性流行模型的数值解。为确保数值格式的可靠性和有效性，通过建立一些标准结果给出了正性、一致性以及线性和非线性稳定性。绘制了模拟图以研究疾病动态的非线性行为。所有图形都描绘了所预测数值格式的正性、有界性和收敛行为。此外，数值图还反映了基本再生数(R_0)在达到稳态中的作用。文章最后给出了该研究的有效成果。
