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Biol."],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Qualitative properties of adequate numerical methods for stochastic differential equations to simulate the stochastic counterparts of some known models with variable contact diffusion rates in mathematical epidemiology are investigated, especially SIS and SIR models with non-constant total population sizes on bounded domains. We show the convergence of numerical approximations based on Balanced Implicit Methods (BIMs) by proving several properties; including positivity, invariance, stability, mean and mean square consistency, local uniform boundedness, mean square H\u00f6lder continuity and mean square contractivity. 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The author\u2019s work complies with international, national and\/or institutional standards of research reporting. We are committed to maintaining the highest level of integrity in the content published.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"The author declares that there is no conflict of interest. There is no financial interest directly or indirectly related to this work, and not any other competing interest.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}}],"article-number":"88"}}