Bulletin of Mathematical Biology

, Volume 80, Issue 4, pp 825–839

# Comments on “A Mathematical Study to Control Visceral Leishmaniasis: An Application to South Sudan”

• E. Iboi
• K. Okuneye
• O. Sharomi
• A. B. Gumel
Original Article

## Abstract

Deterministic (ordinary differential equation) models for the transmission dynamics of vector-borne diseases that incorporate disease-induced death in the host(s) population(s) are generally known to exhibit the phenomenon of backward bifurcation (where a stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number of the model is less than unity). Further, it is well known that, in these models, the phenomenon of backward bifurcation does not occur when the disease-induced death rate is negligible (e.g., if the disease-induced death rate is set to zero). In a recent paper on the transmission dynamics of visceral leishmaniasis (a disease vectored by sandflies), titled “A Mathematical Study to Control Visceral Leishmaniasis: An Application to South Sudan,” published in Bulletin of Mathematical Biology, Vol. 79, Pages 1110–1134, 2017, Ghosh et al. (2017) stated that their deterministic model undergoes a backward bifurcation even when the disease-induced mortality in the host population is set to zero. This result is contrary to the well-established theory on the dynamics of vector-borne diseases. In this short note, we illustrate some of the key errors in the Ghosh et al. (2017) study.

## Keywords

Leishmaniasis Sandflies Reproduction number Backward bifurcation

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