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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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Memory effects in disease modelling through kernel estimates with oscillatory time history.

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This study introduces a new algorithm for analyzing disease spread, showing adaptive behaviors like social distancing can stabilize populations and lower infection rates.

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Area of Science:

  • Mathematical modeling of infectious diseases
  • Dynamical systems theory
  • Epidemiology

Background:

  • Infectious disease models often simplify population behavior.
  • Distributed time delays and memory effects are crucial for realistic disease dynamics.
  • Adaptive behaviors, including non-pharmaceutical interventions, significantly impact disease transmission.

Purpose of the Study:

  • To develop a novel algorithmic framework for analyzing dynamical systems with distributed time delays.
  • To investigate memory effects in population-level disease evolution using SIR and SEIR models.
  • To analyze the stability and impact of adaptive behaviors on disease dynamics.

Main Methods:

  • Design of a linear chain trick algorithm for dynamical systems with oscillatory time histories.
  • Application of the algorithm to susceptible-infected-recovered (SIR) and susceptible-exposed-infected-recovered (SEIR) models.
  • Analysis of system stability and attack rates under adaptive behavior using a history-dependent kernel.

Main Results:

  • The linear chain trick transforms the delayed model into a Markovian system.
  • Adaptive behavior can lead to a stable equilibrium or a stable limit cycle.
  • The model demonstrates a reduced attack rate compared to non-adaptive scenarios.

Conclusions:

  • Adaptive behaviors, modeled via history-dependent kernels, can stabilize disease dynamics.
  • The proposed algorithm effectively analyzes memory effects in epidemiological models.
  • While adaptive behavior offers short-term benefits, its long-term impact diminishes as the disease subsides.