Maria Teresa Signes Pont, Higinio Mora Mora, Antonio Cortés Castillo



A Discrete Approach of the Susceptible-Infectious-Susceptible (SIS) Model of Disease Expansion

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This paper presents a discrete model of the dynamics of infectious disease expansion and builds a link between two conceptually different approaches of the Susceptible-Infectious-Susceptible (SIS) model: the continuous one, depicted by traditional simulation of ordinary differential equations (ODE), and ours, based on both connectivity between individuals and a local binary rule. The connectivity fixes the possible contacts between people and the rule defines whether the contacts are infective or not. The population confines in a grid and contagion extends from the infected centre cell by applying the rule, following the connectivity pattern. Our model provides parameters to tune the rate at which susceptible hosts become infected and the rate at which infected hosts become susceptible. The model has been analyzed and successfully compared to the SIS deterministic compartmental model


Infectious disease expansion, SIS, deterministic compartmental models, ODE, neighbour binary rules, connectivity


[1] Daley, D. J. & Gani, J. Epidemic Modeling: An Introduction. NY: Cambridge Univ. Pr., 2005.

[2] Hethcote, H. W. The mathematics of infectious diseases. Society for Industrial and Applied Mathematics, 42, 599 – 653, 2000.

[3] Bernoulli, D. & Blower, S. An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it. Rev. Medical Virology, 14, 275 – 288, 2004.

[4] Ross R. The Prevention of Malaria. Murray, London, 1911

[5] Kermack, W.O & McKendrick, A.G. A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond. 115 (1927).

[6] Isea, R & Lonngren, K.E. On the Mathematical Interpretation of Epidemics by Kermack and McKendrick. Gen. Math. Notes, Vol. 19, No. 2, December 2013, pp. 83-87.

[7] Brauer, F. & Castillo-Chávez, C. (2001). Mathematical Models in Population Biology and Epidemiology. NY: Springer.

[8] Signes Pont, M.T. at al., The SusceptibleInfectious-Recovered (SIR) model of disease expansion: a new approach. Proc. of the 17th Mathematical Modelling Conference, 2017.

[9] Signes Pont, M.T. at al., The SusceptibleInfectious Model of Disease Expansion analysed under the scope of connectivity and neighbor rules. Computer Science & Information Technology (CS & IT) 7 (1): 1-10, 2017.

Cite this paper

Maria Teresa Signes Pont, Higinio Mora Mora, Antonio Cortés Castillo. (2017) A Discrete Approach of the Susceptible-Infectious-Susceptible (SIS) Model of Disease Expansion. International Journal of Computers, 2, 123-128


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