Open AccessDynamical Analysis on A Model of Cholera Epidemic with Quarantine, Vaccination, and Two Path of Transmissions
Author(s) -
Lilis Suryani,
Wuryansari Muharini Kusumawinahyu,
Nur Shofianah
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1776/1/012052
Subject(s) - equilibrium point , basic reproduction number , epidemic model , stability theory , quarantine , disease transmission , transmission (telecommunications) , mathematical economics , stability (learning theory) , exponential stability , mathematics , point (geometry) , computer science , biology , physics , virology , mathematical analysis , demography , ecology , nonlinear system , sociology , population , telecommunications , geometry , quantum mechanics , machine learning , differential equation
This research focus on dynamical analysis of a SIQRVB (Susceptible-Infectious-Quarantined-Recovered-Vaccinated-Bacterial) model. It describe the spread of cholerae with quarantine, vaccination and two transmission paths. As is well-known, there mainly exist two transmission paths for cholerae: environment-to-human transmission and human-to-human transmission. This model has two equilibrium points, that is disease-free equilibrium point which always exists and an endemic equilibrium point that exists with some conditions. The local stability of the equilibrium points is investigated by using Routh-Hurwitz criteria. The method of Next Generation Matrix is applied to get the basic reproduction number R 0 . It can be shown numerically that disease-free equilibrium point is locally asymptotic stable when R 0 < 1, while the endemic equilibrium point exist and locally asymptotic stable when satisfy Routh-Hurwitz criteria. Numerical simulations are given to illustrate the theoretical results.