TY - JOUR
T1 - Mathematical model for the dynamics of visceral leishmaniasis–malaria co-infection
AU - ELmojtaba, Ibrahim M.
N1 - Publisher Copyright:
Copyright © 2016 John Wiley & Sons, Ltd.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - A mathematical model to understand the dynamics of malaria–visceral leishmaniasis co-infection is proposed and analyzed. Results show that both diseases can be eliminated if R0, the basic reproduction number of the co-infection, is less than unity, and the system undergoes a backward bifurcation where an endemic equilibrium co-exists with the disease-free equilibrium when one of Rm or Rl, the basic reproduction numbers of malaria-only and visceral leishmaniasis-only, is precisely less than unity. Results also show that in the case of maximum protection against visceral leishmaniasis (VL), the disease-free equilibrium is globally asymptotically stable if malaria patients are protected from VL infection; similarly, in the case of maximum protection against malaria, the disease-free equilibrium is globally asymptotically stable if VL and post-kala-azar dermal leishmaniasis patients and the recovered humans after VL are protected from malaria infection. Numerical results show that if Rm and Rl are greater than unity, then we have co-existence of both disease at an endemic equilibrium, and malaria incidence is higher than visceral leishmaniasis incidence at steady state.
AB - A mathematical model to understand the dynamics of malaria–visceral leishmaniasis co-infection is proposed and analyzed. Results show that both diseases can be eliminated if R0, the basic reproduction number of the co-infection, is less than unity, and the system undergoes a backward bifurcation where an endemic equilibrium co-exists with the disease-free equilibrium when one of Rm or Rl, the basic reproduction numbers of malaria-only and visceral leishmaniasis-only, is precisely less than unity. Results also show that in the case of maximum protection against visceral leishmaniasis (VL), the disease-free equilibrium is globally asymptotically stable if malaria patients are protected from VL infection; similarly, in the case of maximum protection against malaria, the disease-free equilibrium is globally asymptotically stable if VL and post-kala-azar dermal leishmaniasis patients and the recovered humans after VL are protected from malaria infection. Numerical results show that if Rm and Rl are greater than unity, then we have co-existence of both disease at an endemic equilibrium, and malaria incidence is higher than visceral leishmaniasis incidence at steady state.
KW - backward bifurcation
KW - basic reproduction number
KW - co-infection
KW - malaria
KW - PKDL
KW - visceral leishmaniasis
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U2 - 10.1002/mma.3864
DO - 10.1002/mma.3864
M3 - Article
AN - SCOPUS:84985914207
SN - 0170-4214
VL - 39
SP - 4334
EP - 4353
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 15
ER -