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Mathematical model for assessing the impact of vaccination and treatment on measles transmission dynamics
Author(s) -
Garba S. M.,
Safi M. A.,
Usaini S.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4462
Subject(s) - mathematics , basic reproduction number , lyapunov function , epidemic model , stability theory , population , transmission (telecommunications) , bifurcation , measles , nonlinear system , statistical physics , mathematical economics , vaccination , demography , physics , biology , computer science , telecommunications , quantum mechanics , sociology , immunology
A deterministic model for the transmission dynamics of measles in a population with fraction of vaccinated individuals is designed and rigorously analyzed. The model with standard incidence exhibits the phenomenon of backward bifurcation, where a stable disease‐free equilibrium coexists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. This phenomenon can be removed if either measles vaccine is assumed to be perfect or disease related mortality rates are negligible. In the latter case, the disease‐free equilibrium is shown to be globally asymptotically stable whenever the associated reproduction number is less than unity. Furthermore, the model has a unique endemic equilibrium whenever the reproduction threshold exceeds unity. This equilibrium is shown, using a nonlinear Lyapunov function of Goh‐Volterra type, to be globally asymptotically stable for a special case.