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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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In this paper, a mathematical dynamical system involving both deterministic (with or without delay) and stochastic ``SIR'' epidemic model with nonlinear incidence rate in a continuous reactor is considered. A profound qualitative analysis is given. It is proved that, for both deterministic models, if $\R_d > 1$, then the endemic equilibrium is globally asymptotically stable. However, if $\R_d \leq 1$, then the disease-free equilibrium is globally asymptotically stable. Concerning the stochastic model, the Feller's test combined with the canonical probability method were used in order to conclude on the long-time dynamics of the stochastic model. The results improve and extend the results obtained for the deterministic model in its both forms. It is proved that if $\R_s > 1$, the disease is stochastically permanent with full probability. However, if $\R_s \leq 1$, then the disease dies out with full probability. Finally, some numerical tests are done in order to validate the obtained results.
목차
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참고문헌 (22)
참고문헌 신청
T. W. Berngruber / 2013 / Evolution of virulence in emerging epidemics / PLoS Pathog 9(3)
G. Birkhoff / 1962 / Ordinary Differential Equations, Introductions to Higher Mathematics / Ginn and Company
B. Bonzi / 2011 / Stability of differential susceptibility and infectivity epidemic models / Journal of Mathematical Biology 62(1):39~64
J. J. Bull / 2006 / Evolutionary feedback mediated through population density, illustrated with viruses in chemostats / American naturalist 167(2):E39~E51
Miled El Hajji / 2019 / How can inter-specific interferences explain coexistence or confirm the competitive exclusion principle in a chemostat? / International Journal of Biomathematics 11(08):1850111
G. Birkhoff / 1962 / Ordinary Differential Equations, Introductions to Higher Mathematics / Ginn and Company
B. Bonzi / 2011 / Stability of differential susceptibility and infectivity epidemic models / Journal of Mathematical Biology 62(1):39~64
J. J. Bull / 2006 / Evolutionary feedback mediated through population density, illustrated with viruses in chemostats / American naturalist 167(2):E39~E51
Miled El Hajji / 2019 / How can inter-specific interferences explain coexistence or confirm the competitive exclusion principle in a chemostat? / International Journal of Biomathematics 11(08):1850111
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