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A general theory for infectious disease dynamics

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  • Carbone, Giuseppe
  • De Vincenzo, Ilario

Abstract

We present a general theory of infection spreading. It directly follows from conservation laws once known the probability density functions of latent times. The theory can deal with any distribution of compartments latent times. Real probability density function can be then employed, thus overcoming the limitations of standard SIR, SEIR and other similar models that implicitly make use of exponential or exponential-related distributions. SIR and SEIR-type models are, in fact, a subclass of the theory here presented. We show that beside the infection rate, the probability density functions of latent times in the exposed and infectious compartments govern the dynamics of infection spreading. We study the stability of such dynamical system and provide the general solution of the linearized equations in terms of the characteristic functions of latent times probability density functions. We exploit the theory to simulate the spreading of COVID-19 infection in Italy during the first 120 days.

Suggested Citation

  • Carbone, Giuseppe & De Vincenzo, Ilario, 2022. "A general theory for infectious disease dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922010396
    DOI: 10.1016/j.chaos.2022.112860
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    References listed on IDEAS

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    1. Helen J Wearing & Pejman Rohani & Matt J Keeling, 2005. "Appropriate Models for the Management of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 2(7), pages 1-1, July.
    2. Benjamin Ivorra & Beatriz Martínez-López & José Sánchez-Vizcaíno & Ángel Ramos, 2014. "Mathematical formulation and validation of the Be-FAST model for Classical Swine Fever Virus spread between and within farms," Annals of Operations Research, Springer, vol. 219(1), pages 25-47, August.
    3. Phenyo E. Lekone & Bärbel F. Finkenstädt, 2006. "Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study," Biometrics, The International Biometric Society, vol. 62(4), pages 1170-1177, December.
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