{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T06:39:25Z","timestamp":1772347165168,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,27]],"date-time":"2021-11-27T00:00:00Z","timestamp":1637971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Background: Nipah virus (NiV) is a zoonotic virus (transmitted from animals to humans), which can also be transmitted through contaminated food or directly between people. According to a World Health Organization (WHO) report, the transmission of Nipah virus infection varies from animals to humans or humans to humans. The case fatality rate is estimated at 40% to 75%. The most infected regions include Cambodia, Ghana, Indonesia, Madagascar, the Philippines, and Thailand. The Nipah virus model is categorized into four parts: susceptible (S), exposed (E), infected (I), and recovered (R). Methods: The structural properties such as dynamical consistency, positivity, and boundedness are the considerable requirements of models in these fields. However, existing numerical methods like Euler\u2013Maruyama and Stochastic Runge\u2013Kutta fail to explain the main features of the biological problems. Results: The proposed stochastic non-standard finite difference (NSFD) employs standard and non-standard approaches in the numerical solution of the model, with positivity and boundedness as the characteristic determinants for efficiency and low-cost approximations. While the results from the existing standard stochastic methods converge conditionally or diverge in the long run, the solution by the stochastic NSFD method is stable and convergent over all time steps. Conclusions: The stochastic NSFD is an efficient, cost-effective method that accommodates all the desired feasible properties.<\/jats:p>","DOI":"10.3390\/e23121588","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T05:23:02Z","timestamp":1638163382000},"page":"1588","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Breakdown of a Nonlinear Stochastic Nipah Virus Epidemic Models through Efficient Numerical Methods"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6443-9966","authenticated-orcid":false,"given":"Ali","family":"Raza","sequence":"first","affiliation":[{"name":"Department of Mathematics, Govt. Maulana Zafar Ali Khan Graduate College Wazirabad, Punjab Higher Education Department (PHED), Lahore 54000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0387-921X","authenticated-orcid":false,"given":"Jan","family":"Awrejcewicz","sequence":"additional","affiliation":[{"name":"Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1\/15 Stefanowskiego St., 90-924 Lodz, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2165-3479","authenticated-orcid":false,"given":"Muhammad","family":"Rafiq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore 54600, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6415-7128","authenticated-orcid":false,"given":"Muhammad","family":"Mohsin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Technische Universitat Chemnitz, 62, 09111 Chemnitz, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,27]]},"reference":[{"key":"ref_1","first-page":"77","article-title":"Epidemiological aspects of nipah virus infection","volume":"4","author":"Tan","year":"1999","journal-title":"Neurol. 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