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Continuous and discrete approaches to the epidemiology of viral spreading in populations taking into account the delay of incubation time

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  • Monteiro, L.H.A.
  • Sasso, J.B.
  • Chaui Berlinck, J.G.

Abstract

A significant part of theoretical approaches to model viral spreading diseases in populations does not take into account the time delay between the contact with the viral particles and the transmitting state of the host. The question then becomes whether such a biological fact must become part of these models or not; thus imparing many theoretical reports. Also, ecological systems, as human agglomerates, are not spatialy homogeneous, and the ordinary differential equations to simulate these systems are subjected to assumptions which can be unrealistic, many times. Here we study the spreading of a viral contagious disease in a population of constant size using epidemiological models described in terms of delay differential equations and probabilistic cellular automata. The delay represents the characteristic time between a susceptible individual to acquire the virus and to become a transmitter of it. We conclude that such a delay does not affect the local stability of the equilibrium solutions in both approaches.

Suggested Citation

  • Monteiro, L.H.A. & Sasso, J.B. & Chaui Berlinck, J.G., 2007. "Continuous and discrete approaches to the epidemiology of viral spreading in populations taking into account the delay of incubation time," Ecological Modelling, Elsevier, vol. 201(3), pages 553-557.
  • Handle: RePEc:eee:ecomod:v:201:y:2007:i:3:p:553-557
    DOI: 10.1016/j.ecolmodel.2006.09.027
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    References listed on IDEAS

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    1. Willox, R. & Grammaticos, B. & Carstea, A.S. & Ramani, A., 2003. "Epidemic dynamics: discrete-time and cellular automaton models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 13-22.
    2. Fuentes, M.A. & Kuperman, M.N., 1999. "Cellular automata and epidemiological models with spatial dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 267(3), pages 471-486.
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    Cited by:

    1. Pereira, F.M.M. & Schimit, P.H.T., 2018. "Dengue fever spreading based on probabilistic cellular automata with two lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 75-87.
    2. Schimit, P.H.T. & Monteiro, L.H.A., 2010. "Who should wear mask against airborne infections? Altering the contact network for controlling the spread of contagious diseases," Ecological Modelling, Elsevier, vol. 221(9), pages 1329-1332.
    3. Schimit, P.H.T. & Monteiro, L.H.A., 2009. "On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata," Ecological Modelling, Elsevier, vol. 220(7), pages 1034-1042.
    4. Ramos, A.B.M. & Schimit, P.H.T., 2019. "Disease spreading on populations structured by groups," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 265-273.

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