TY - JOUR
T1 - Qualitative Stability Analysis of an Obesity Epidemic Model with Social Contagion
AU - Lozano-Ochoa, Enrique
AU - Camacho, Jorge Fernando
AU - Vargas-De-León, Cruz
N1 - Publisher Copyright:
© 2017 Enrique Lozano-Ochoa et al.
PY - 2017
Y1 - 2017
N2 - We study an epidemiological mathematical model formulated in terms of an ODE system taking into account both social and nonsocial contagion risks of obesity. Analyzing first the case in which the model presents only the effect due to social contagion and using qualitative methods of the stability analysis, we prove that such system has at the most three equilibrium points, one disease-free equilibrium and two endemic equilibria, and also that it has no periodic orbits. Particularly, we found that when considering R0 (the basic reproductive number) as a parameter, the system exhibits a backward bifurcation: the disease-free equilibrium is stable when R0<1 and unstable when R0>1, whereas the two endemic equilibria appear from R0 (a specific positive value reached by R0 and less than unity), one being asymptotically stable and the other unstable, but for R0>1 values, only the former remains inside the feasible region. On the other hand, considering social and nonsocial contagion and following the same methodology, we found that the dynamic of the model is simpler than that described above: it has a unique endemic equilibrium point that is globally asymptotically stable.
AB - We study an epidemiological mathematical model formulated in terms of an ODE system taking into account both social and nonsocial contagion risks of obesity. Analyzing first the case in which the model presents only the effect due to social contagion and using qualitative methods of the stability analysis, we prove that such system has at the most three equilibrium points, one disease-free equilibrium and two endemic equilibria, and also that it has no periodic orbits. Particularly, we found that when considering R0 (the basic reproductive number) as a parameter, the system exhibits a backward bifurcation: the disease-free equilibrium is stable when R0<1 and unstable when R0>1, whereas the two endemic equilibria appear from R0 (a specific positive value reached by R0 and less than unity), one being asymptotically stable and the other unstable, but for R0>1 values, only the former remains inside the feasible region. On the other hand, considering social and nonsocial contagion and following the same methodology, we found that the dynamic of the model is simpler than that described above: it has a unique endemic equilibrium point that is globally asymptotically stable.
UR - http://www.scopus.com/inward/record.url?scp=85012118466&partnerID=8YFLogxK
U2 - 10.1155/2017/1084769
DO - 10.1155/2017/1084769
M3 - Artículo
SN - 1026-0226
VL - 2017
JO - Discrete Dynamics in Nature and Society
JF - Discrete Dynamics in Nature and Society
M1 - 1084769
ER -