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We focus on the evolution of a new more aggressive mutant strain that appears at specific nodes in the system and competes with a previous version until reaching fixation. The role of host-interaction network topology in the emergence and spatial diffusion of these highly contagious strains is analyzed, as well as how network-based interventions can help mitigate their spread. To address these issues, we present simplified mathematical models that qualitatively describe the occurrence, propagation, and impact of such mutations within host-interaction networks. By incorporating the heterogeneous topology of the host network into the analysis, a more advanced framework is proposed to curb the growth of mutant strains. Extensive numerical simulations of these models offer insights into the mechanisms driving viral evolution, the dynamics of contagion, and the critical topological influence of the initial seed nodes under different kinetic regimes, providing a robust perspective on viral spread and containment strategies.<\/jats:p>","DOI":"10.1063\/5.0333746","type":"journal-article","created":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T15:50:38Z","timestamp":1783007438000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Topological dependence of viral mutation spread in complex host-interaction networks"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5151-6184","authenticated-orcid":false,"given":"Javier","family":"L\u00f3pez-Pedrares","sequence":"first","affiliation":[{"name":"Department of Mathematics, Universidade de Vigo 1 , 36310 Vigo,","place":["Spain"]},{"name":"Group of Nonlinear Physics, Universidade de Santiago de Compostela 2 , 15782 Santiago de Compostela,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6954-6747","authenticated-orcid":false,"given":"M. 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