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For this dynamics model, the novel coronavirus COVID-19, a contagious disease, is taken as a case study in which its transmission, impact of vaccination, and mitigation have been discussed. This model may be helpful in numerous fields of epidemiology and dynamical systems; moreover, Mason Graph has been used to describe the mathematical model. The stability analysis and disease-free equilibrium points have been deliberated for the model. In this work, the semi-analytical technique Variational Iteration Method has been employed, which will assist researchers in the future by showing that if the rate of immunized personnel rises, then the infection rate decreases. It has been observed that the non-vaccinated personnel decrease with the passage of time due to the awareness campaign programs of the governments. Furthermore, it was observed that the removed rate also decreases with the passage of time as the immunized personnel rises. Mathematical software MAPLE has been used to calculate the analytical solutions of the aforementioned mathematical model.<\/jats:p>","DOI":"10.1038\/s41598-025-34692-y","type":"journal-article","created":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T14:07:23Z","timestamp":1767708443000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Nonlinear compartmental modeling of COVID-19 with dual dose vaccination using Mason graphs and variational iteration method"],"prefix":"10.1038","volume":"16","author":[{"given":"Umer","family":"Ghani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bilal","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shahid","family":"Mahmood","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aymen","family":"Flah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad","family":"Ghatasheh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ivo","family":"Pergl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,6]]},"reference":[{"key":"34692_CR1","doi-asserted-by":"publisher","first-page":"S223","DOI":"10.1097\/01.inf.0000188166.17324.60","volume":"24","author":"JS Kahn","year":"2005","unstructured":"Kahn, J. 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