EFFECT OF DELAY ON THE MODEL OF AMERICAN CUTANEOUS LEISHMANIASIS

This paper investigates the dynamics of transmission of a model of American cutaneous leishmaniasis (ACL). The model consists of infectious incidental hosts (humans), reservoir hosts (forest rodents, dogs, etc.) and vectors. A delay in the time between infection and infectiousness for the reservoir hosts is incorporated. In the absence of delay, it is observed that if R0 > 1, then endemic equilibrium becomes stable and if R0 < 1 then infection-free equilibrium becomes stable. The length of delay is estimated for preserving stability. Stability switching behavior of the system is also indicated. Lastly the results are verified through numerical simulations as far as possible.

[1]  R. Reithinger,et al.  The transmission dynamics of canine American cutaneous leishmaniasis in Huánuco, Peru. , 2003, The American journal of tropical medicine and hygiene.

[2]  P. Coleman,et al.  Are insecticide-impregnated dog collars a feasible alternative to dog culling as a strategy for controlling canine visceral leishmaniasis in Brazil? , 2004, International journal for parasitology.

[3]  L. F. Chaves,et al.  Mathematical modelling of American cutaneous leishmaniasis: incidental hosts and threshold conditions for infection persistence. , 2004, Acta tropica.

[4]  L. Rodrigues,et al.  Indoor and peridomestic transmission of American cutaneous leishmaniasis in northwestern Argentina: a retrospective case-control study. , 2003, The American journal of tropical medicine and hygiene.

[5]  D. R. Martins,et al.  Changing epidemiology of American cutaneous leishmaniasis (ACL) in Brazil: a disease of the urban-rural interface. , 2004, Acta tropica.

[6]  B. Gontijo,et al.  Leishmaniose tegumentar americana , 2003 .

[7]  M. Maroli,et al.  [Prevention and control of leishmaniasis vectors: current approaches]. , 2004, Parassitologia.

[8]  Eduardo Massad,et al.  Modelling the Dynamics of Leishmaniasis Considering Human, Animal Host and Vector Populations , 1998 .

[9]  W. Caiaffa,et al.  Risk factors for mucosal manifestation of American cutaneous leishmaniasis. , 2005, Transactions of the Royal Society of Tropical Medicine and Hygiene.

[10]  C. Dye,et al.  The logic of visceral leishmaniasis control. , 1996, The American journal of tropical medicine and hygiene.

[11]  C. Dye,et al.  Mathematical modelling and theory for estimating the basic reproduction number of canine leishmaniasis , 1992, Parasitology.

[12]  P. Desjeux,et al.  Estimation of population at risk of infection and number of cases of Leishmaniasis. , 1992, Parasitology today.

[13]  M. Feliciangeli,et al.  Parameters of Leishmania braziliensis transmission by indoor Lutzomyia ovallesi in Venezuela. , 2004, The American journal of tropical medicine and hygiene.

[14]  R. Lainson,et al.  Clinical and immunopathological spectrum of American cutaneous leishmaniasis with special reference to the disease in Amazonian Brazil: a review. , 2004, Memorias do Instituto Oswaldo Cruz.