Journal of Mathematical Biology

, Volume 53, Issue 3, pp 421–436 | Cite as

The epidemic threshold of vector-borne diseases with seasonality

The case of cutaneous leishmaniasis in Chichaoua, Morocco
  • Nicolas Bacaër
  • Souad Guernaoui


Cutaneous leishmaniasis is a vector-borne disease transmitted to humans by sandflies. In this paper, we develop a mathematical model which takes into account the seasonality of the vector population and the distribution of the latent period from infection to symptoms in humans. Parameters are fitted to real data from the province of Chichaoua, Morocco. We also introduce a generalization of the definition of the basic reproduction number R 0 which is adapted to periodic environments. This R 0 is estimated numerically for the epidemic in Chichaoua; \(R_0\simeq\) 1.94. The model suggests that the epidemic could be stopped if the vector population were reduced by a factor \((R_0)^2\simeq\) 3.76.


Vector-borne disease Seasonality Epidemic threshold 

Mathematics Subject Classification (2000)

92D30 35Q80 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.IRDBondyFrance
  2. 2.Laboratoire d’Ecologie Animale TerrestreFaculté des Sciences SemlaliaMarrakechMorocco

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