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New global dynamical results and application of several SVEIS epidemic models with temporary immunity. (English) Zbl 07330185
Summary: This work applies a novel geometric criterion for global stability of nonlinear autonomous differential equations generalized by G. Lu and Z. Lu [Nonlinear Anal., Real World Appl. 36, 20–43 (2017; Zbl 1379.34043)] to establish global threshold dynamics for several SVEIS epidemic models with temporary immunity, incorporating saturated incidence and nonmonotone incidence with psychological effect, and an SVEIS model with saturated incidence and partial temporary immunity. Incidentally, global stability for the SVEIS models with saturated incidence in [L.-M. Cai and X.-Z. Li, Appl. Math. Modelling 33, No. 7, 2919–2926 (2009; Zbl 1205.34049); G. P. Sahu and J. Dhar, ibid. 36, No. 3, 908–923 (2012; Zbl 1243.34068)] is completely solved. Furthermore, employing the DEDiscover simulation tool, the parameters in Sahu and Dhar’model are estimated with the 2009–2010 pandemic H1N1 case data in Hong Kong China, and it is validated that the vaccination programme indeed avoided subsequent potential outbreak waves of the pandemic. Finally, global sensitivity analysis reveals that multiple control measures should be utilized jointly to cut down the peak of the waves dramatically and delay the arrival of the second wave, thereinto timely vaccination is particularly effective.
MSC:
92 Biology and other natural sciences
37 Dynamical systems and ergodic theory
Software:
DEDiscover
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References:
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