### Abstract

Zoonotic visceral leishmaniasis (ZVL), caused by the protozoan parasite Leishmania infantum and transmitted to humans and reservoir hosts by female sandflies, is endemic in many parts of the world (notably in Africa, Asia and the Mediterranean). This study presents a new mathematical model for assessing the transmission dynamics of ZVL in human and non-human animal reservoir populations. The model undergoes the usual phenomenon of backward bifurcation exhibited by similar vector-borne disease transmission models. In the absence of such phenomenon (which is shown to arise due to the disease-induced mortality in the host populations), the nontrivial disease-free equilibrium of the model is shown to be globally-asymptotically stable when the associated reproduction number of the model is less than unity. Using case and demographic data relevant to ZVL dynamics in Arac̣atuba municipality of Brazil, it is shown, for the default case when systemic insecticide-based drugs are not used to treat infected reservoir hosts, that the associated reproduction number of the model (ℛ_{0}) ranges from 0.3 to 1.4, with a mean of ℛ_{0}=0.85. Furthermore, when the effect of such drug treatment is explicitly incorporated in the model (i.e., accounting for the additional larval and sandfly mortality, following feeding on the treated reservoirs), the range of ℛ_{0} decreases to ℛ_{0}∈[0.1,0.6], with a mean of ℛ_{0}=0.35 (this significantly increases the prospect of the effective control or elimination of the disease). Thus, ZVL transmission models (in communities where such treatment strategy is implemented) that do not explicitly incorporate the effect of such treatment may be over-estimating the disease burden (as measured in terms of ℛ_{0}) in the community. It is shown that ℛ_{0} is more sensitive to increases in sandfly lifespan than that of the animal reservoir (so, a strategy that focuses on reducing sandflies, rather than the animal reservoir (e.g., via culling), may be more effective in reducing ZVL burden in the community). Further sensitivity analysis of the model ranks the sandfly removal rate (by natural death or by feeding from insecticide-treated reservoir hosts), the biting rate of sandflies on the reservoir hosts and the progression rate of exposed reservoirs to active ZVL as the three parameters with the most effect on the disease dynamics or burden (as measured in terms of the reproduction number ℛ_{0}). Hence, this study identifies the key parameters that play a key role on the disease dynamics, and thereby contributing in the design of effective control strategies (that target the identified parameters).

Original language | English (US) |
---|---|

Pages (from-to) | 455-474 |

Number of pages | 20 |

Journal | Infectious Disease Modelling |

Volume | 2 |

Issue number | 4 |

DOIs | |

State | Published - Nov 1 2017 |

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### Keywords

- Backward bifurcation
- Leishmania infantum
- Reproduction number
- Stability
- Zoonotic visceral leishmaniasis (ZVL)

### ASJC Scopus subject areas

- Infectious Diseases
- Applied Mathematics
- Health Policy

### Cite this

*Infectious Disease Modelling*,

*2*(4), 455-474. https://doi.org/10.1016/j.idm.2017.12.002

**Mathematical analysis of a model for zoonotic visceral leishmaniasis.** / Hussaini, Nafiu; Okuneye, Kamaldeen; Gumel, Abba.

Research output: Contribution to journal › Article

*Infectious Disease Modelling*, vol. 2, no. 4, pp. 455-474. https://doi.org/10.1016/j.idm.2017.12.002

}

TY - JOUR

T1 - Mathematical analysis of a model for zoonotic visceral leishmaniasis

AU - Hussaini, Nafiu

AU - Okuneye, Kamaldeen

AU - Gumel, Abba

PY - 2017/11/1

Y1 - 2017/11/1

N2 - Zoonotic visceral leishmaniasis (ZVL), caused by the protozoan parasite Leishmania infantum and transmitted to humans and reservoir hosts by female sandflies, is endemic in many parts of the world (notably in Africa, Asia and the Mediterranean). This study presents a new mathematical model for assessing the transmission dynamics of ZVL in human and non-human animal reservoir populations. The model undergoes the usual phenomenon of backward bifurcation exhibited by similar vector-borne disease transmission models. In the absence of such phenomenon (which is shown to arise due to the disease-induced mortality in the host populations), the nontrivial disease-free equilibrium of the model is shown to be globally-asymptotically stable when the associated reproduction number of the model is less than unity. Using case and demographic data relevant to ZVL dynamics in Arac̣atuba municipality of Brazil, it is shown, for the default case when systemic insecticide-based drugs are not used to treat infected reservoir hosts, that the associated reproduction number of the model (ℛ0) ranges from 0.3 to 1.4, with a mean of ℛ0=0.85. Furthermore, when the effect of such drug treatment is explicitly incorporated in the model (i.e., accounting for the additional larval and sandfly mortality, following feeding on the treated reservoirs), the range of ℛ0 decreases to ℛ0∈[0.1,0.6], with a mean of ℛ0=0.35 (this significantly increases the prospect of the effective control or elimination of the disease). Thus, ZVL transmission models (in communities where such treatment strategy is implemented) that do not explicitly incorporate the effect of such treatment may be over-estimating the disease burden (as measured in terms of ℛ0) in the community. It is shown that ℛ0 is more sensitive to increases in sandfly lifespan than that of the animal reservoir (so, a strategy that focuses on reducing sandflies, rather than the animal reservoir (e.g., via culling), may be more effective in reducing ZVL burden in the community). Further sensitivity analysis of the model ranks the sandfly removal rate (by natural death or by feeding from insecticide-treated reservoir hosts), the biting rate of sandflies on the reservoir hosts and the progression rate of exposed reservoirs to active ZVL as the three parameters with the most effect on the disease dynamics or burden (as measured in terms of the reproduction number ℛ0). Hence, this study identifies the key parameters that play a key role on the disease dynamics, and thereby contributing in the design of effective control strategies (that target the identified parameters).

AB - Zoonotic visceral leishmaniasis (ZVL), caused by the protozoan parasite Leishmania infantum and transmitted to humans and reservoir hosts by female sandflies, is endemic in many parts of the world (notably in Africa, Asia and the Mediterranean). This study presents a new mathematical model for assessing the transmission dynamics of ZVL in human and non-human animal reservoir populations. The model undergoes the usual phenomenon of backward bifurcation exhibited by similar vector-borne disease transmission models. In the absence of such phenomenon (which is shown to arise due to the disease-induced mortality in the host populations), the nontrivial disease-free equilibrium of the model is shown to be globally-asymptotically stable when the associated reproduction number of the model is less than unity. Using case and demographic data relevant to ZVL dynamics in Arac̣atuba municipality of Brazil, it is shown, for the default case when systemic insecticide-based drugs are not used to treat infected reservoir hosts, that the associated reproduction number of the model (ℛ0) ranges from 0.3 to 1.4, with a mean of ℛ0=0.85. Furthermore, when the effect of such drug treatment is explicitly incorporated in the model (i.e., accounting for the additional larval and sandfly mortality, following feeding on the treated reservoirs), the range of ℛ0 decreases to ℛ0∈[0.1,0.6], with a mean of ℛ0=0.35 (this significantly increases the prospect of the effective control or elimination of the disease). Thus, ZVL transmission models (in communities where such treatment strategy is implemented) that do not explicitly incorporate the effect of such treatment may be over-estimating the disease burden (as measured in terms of ℛ0) in the community. It is shown that ℛ0 is more sensitive to increases in sandfly lifespan than that of the animal reservoir (so, a strategy that focuses on reducing sandflies, rather than the animal reservoir (e.g., via culling), may be more effective in reducing ZVL burden in the community). Further sensitivity analysis of the model ranks the sandfly removal rate (by natural death or by feeding from insecticide-treated reservoir hosts), the biting rate of sandflies on the reservoir hosts and the progression rate of exposed reservoirs to active ZVL as the three parameters with the most effect on the disease dynamics or burden (as measured in terms of the reproduction number ℛ0). Hence, this study identifies the key parameters that play a key role on the disease dynamics, and thereby contributing in the design of effective control strategies (that target the identified parameters).

KW - Backward bifurcation

KW - Leishmania infantum

KW - Reproduction number

KW - Stability

KW - Zoonotic visceral leishmaniasis (ZVL)

UR - http://www.scopus.com/inward/record.url?scp=85064907818&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064907818&partnerID=8YFLogxK

U2 - 10.1016/j.idm.2017.12.002

DO - 10.1016/j.idm.2017.12.002

M3 - Article

VL - 2

SP - 455

EP - 474

JO - Infectious Disease Modelling

JF - Infectious Disease Modelling

SN - 2468-0427

IS - 4

ER -