The outbreak of infectious diseases is the result of a combination of various factors, including season, the movement of individuals, non-pharmaceutical interventions (NPIs) and the effectiveness and availability of vaccines. Taking these key elements into consideration, an almost periodic SVEIR warning model in the patch environment is here proposed. First, in terms of reproduction numbers, our results imply that if the effective reproduction numbers are $R_{e}<1$, then the disease dies out; if $R_{e}>1$, then the disease spreads and leads to local outbreaks. Second, the relationships between $R_{e}$ and $C_{s1}$, $C_{a1}$ (see Section 2) are given by numerical simulations. The numerical results show that even if all people are vaccinated, NPIs are still needed because of the potentially low efficacy of vaccines. Furthermore, the numerical results suggest that NPIs and the strengthening of the effective rate of vaccination are essential in order to achieve herd immunity. Theories involving this model effectively explain the transmission mechanism of most infectious diseases, and provide a valuable theoretical basis for analyzing new infectious diseases in the future. Moreover, this model is helpful for the prevention and control of infectious diseases and the formulation of public health safety policies.
Binguo WANG1
,
*
,
Xiaomei MA1
,
Yashi WANG2
. THE DYNAMICAL BEHAVIOR OF AN ALMOST PERIODIC SVEIR WARNING MODEL IN A PATCHY ENVIRONMENT[J]. Acta mathematica scientia, Series B, 2026
, 46(1)
: 427
-458
.
DOI: 10.1007/s10473-026-0123-4
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