An integral renewal equation approach to behavioural epidemic models with information index
arxiv(2024)
摘要
We propose an integral model describing an epidemic of an infectious disease.
The model is behavioural in the sense that the constitutive law for the force
of infection includes a distributed delay, called "information index", that
describes the opinion-driven human behavioural changes. The information index,
in turn, contains a memory kernel to mimic how the individuals maintain memory
of the past values of the infection. We obtain sufficient conditions for the
endemic equilibrium to be locally stable. In particular, we show that when the
infectivity function is represented by an exponential distribution, stability
is guaranteed by the weak Erlang memory kernel. However, through numerical
simulations, we show that self-sustained oscillations may arise when the memory
is more focused in the disease's past history, as exemplified by the strong
Erlang kernel. We also show the model solutions in cases of different
infectivity functions describing infectious diseases like influenza and SARS.
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