Spread in time of some bacterial infectious diseases: a mathematical model
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enfermedades infecciosas
ecuaciones no lineales de retraso
comportamiento asintónico Infectious diseases
nonlinear delay equations
asymptotic behavior

How to Cite

Cipolatti, R., López Gondar, J., & Siqueira, E. (2014). Spread in time of some bacterial infectious diseases: a mathematical model. Nova Scientia, 4(8), 42–65. https://doi.org/10.21640/ns.v4i8.167


We introduce a new theoretical model to describe the dynamics of transmission for a certain class of bacterial infectious diseases. The propagation mechanism considered is the one concerning direct personal contact. Immunity factors, if present, will be ignored, but in our calculations is included the existence of an incubation period for the contagious infection. The effects of public health campaigns on the spread of the disease are also considered and the inclusion of a certain parameter ε to measure the effciency of such attempts is proposed.
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Bailey, N.J.T.: The mathematical theory of infectious diseases and its applications; Griffin, London, 1975.

Bellmann, R., Cooke, K.L.: Differential-difference equations; Math. in Sciences and Engineering, Academic Press, 1963.

Capasso, V.: Mathematical structure of epidemic systems ; Springer-Verlag, 1993. [4] Cipolatti, R., Lo´pez Gondar, J.: Dynamics of a virtual virus infection process in volving a spatial distribution of interacting computers ; Applicable Analysis: An International Journal, 1563-504X, Volume 84, Issue 1, (2005,) pp. 49–65.

Cooke, K.L., Yorke, J.A.: Some equations modelling growth processes and gonorrhea epidemics ; Mathematical Biosciences, #16 (1973), pp. 75–101.

Cui, C., Sun, Y., Zhu, H.: The impact of media on the control of infectious diseases; Journal of Dynamics and Differential Equations, Vol. 20, No. 1, (2008), pp. 31-53.

Driver, R.D.: Ordinary and delay differential equations ; Applied Mathematical

Sciences #20, Springer-Verlag, 1977.

Diekmann, O., Heesterbeek, J.A.P.: Mathematical epidemiology of infectious diseases. Model building, analysis and interpretation ; John Wiley & Sons, Ltd., Chischester, 2000.

Lo´pez Gondar, J., Cipolatti, R.: A mathematical model for virus infectious in a system of interacting computers; Comp. Appl. Math., Vol. 22, No. 2, (2003), 209-231.

Ghosh, M., Chandra, P., Sinha, P., Shukla, J.B.: Modelling the spread of bacterial infectious disease with environmental effect in a logistically growing human population; Nonlinear Anaysis: Real World Applications, No. 7, (2006), 341–363.

Hale, J.: Theory of functional differential equations ; Applied Mathematical Sciences #3, Springer-Verlag, 1977.

Hethcode, H.D., Tudor, D.W.: Integral equation models for endemic infectious diseases ; Journal of Mathematical Biology, No. 9, (1980), 37–47.

Hethcode, H.D., Stech, H.W., Driessch, P.: Stability analysis for models of diseases without immunity ; Journal of Mathematical Biology, No. 13, (1981), 185–198.

Li, J., Zou, X.: Modeling spatial spread of infectious diseases with a fixed latent period in a spatially continuous domain ; Bulletin of Mathematical Biology, Vol. 71, (2009), 2048–2079.

Liu, Y., Cui, J.A.: The impact of media coverage on the dynamics of infectiuous disease ; International Journal of Biomathematics, V. 1, No. 1, (2008), 65-74.

Mohtashemi, M., Levins, R.: Transient dynamics and early diagnostics in infectious diseases ; Journal of Mathematical Biology, Vol. 43, (2001), pp. 446-470.

Niculescu, S-I., Kim, P.S., Gu, K., Lee, P.P., Levy, D.: Stability crossing boundaries of delay systems modeling immune dynamics in leukemia ; Discrete and Continuous Dynamic Systems, serie B, V. 10, No. 1, (2010), 129–156

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