Global Stability and Backward Bifurcation for a Lymphatic filariasis model

Abstract

An ODE model of Lymphatic filariasis is proposed with eight mutually disjoint compartments. The model is proven to be mathematically and epidemiologically well posed. Epidemiological interpretation of the effective reproduction number is presented. A special case is considered where the death rate due to the disease is negligible. An endemic equilibrium under this special scenario is explicitly computed and the presence of backward bifurcation under this condition is suggested. Bifurcation analysis is performed using the Castillo-Chavez and Song theorem in the special case where death due to disease is zero. When the re-infection rate is zero, backward bifurcation is shown not to be present. In such a situation, global asymptotic stability of the endemic equilibrium is established.

A game-theoretic model of lymphatic filariasis prevention

“…[ 23 ] constructed an SEIQ-SI LF model with quarantine and treatment as control strategies. Also, [ 24 ] modeled LF-tuberculosis coinfections and [ 25 ] considered global stability and backward bifurcation of their LF transmission model. The cost-effectiveness of different intervention strategies is considered in [ 26 ].…”