{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T20:33:48Z","timestamp":1759091628666,"version":"3.41.2"},"reference-count":39,"publisher":"World Scientific Pub Co Pte Ltd","issue":"15","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2021,12,15]]},"abstract":"<jats:p> The study of epidemiological systems has generated deep interest in exploring the dynamical complexity of common infectious diseases driven by seasonally varying contact rates. Mathematical modeling and field observations have shown that, under seasonal variation, the incidence rates of some endemic infectious diseases fluctuate dramatically and the dynamics is often characterized by chaotic oscillations in the absence of specific vaccination programs. In fact, the existence of chaotic behavior has been precisely stated in the literature as a noticeable feature in the dynamics of the classical Susceptible-Infected-Recovered (SIR) seasonally forced epidemic model. However, in the context of epidemiology, chaos is often regarded as an undesirable phenomenon associated with the unpredictability of infectious diseases. As a consequence, the problem of converting chaotic motions into regular motions becomes particularly relevant. In this article, we consider the so-called phase control method applied to the seasonally forced SIR epidemic model to suppress chaos. Interestingly, this method of controlling chaos has a clear meaning as a weak perturbation on a seasonal vaccination strategy. Numerical simulations show that the phase difference between the two periodic forces \u2014 contact rate and vaccination \u2014 plays a very important role in controlling chaos. <\/jats:p>","DOI":"10.1142\/s0218127421300445","type":"journal-article","created":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T11:30:05Z","timestamp":1638876605000},"source":"Crossref","is-referenced-by-count":5,"title":["Controlling Infectious Diseases: The Decisive Phase Effect on a Seasonal Vaccination Strategy"],"prefix":"10.1142","volume":"31","author":[{"given":"Jorge","family":"Duarte","sequence":"first","affiliation":[{"name":"ISEL \u2013 Engineering Superior Institute of Lisbon, Department of Mathematics, Rua Conselheiro Em\u00eddio Navarro 1, 1950-007 Lisboa, Portugal"},{"name":"Centre for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001, Portugal"}]},{"given":"Cristina","family":"Janu\u00e1rio","sequence":"additional","affiliation":[{"name":"ISEL \u2013 Engineering Superior Institute of Lisbon, Department of Mathematics, Rua Conselheiro Em\u00eddio Navarro 1, 1950-007 Lisboa, Portugal"},{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"given":"Nuno","family":"Martins","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal"}]},{"given":"Jes\u00fas M.","family":"Seoane","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamics and Chaos Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s\/n 28933 M\u00f3stoles, Madrid, Spain"}]},{"given":"Miguel A. 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