Dynamic Analysis of Epidemic Model for Cholera Disease Spreading with Quarantine

Aruman Imron,Tyas Husadaningsih,Wuryansari Muharini K

doi:10.21776/ub.jels.2018.008.01.03

Aruman Imron, Tyas Husadaningsih + Show 1 more

Open Access

https://doi.org/10.21776/ub.jels.2018.008.01.03

Copy DOI

Abstract

In this paper, the epidemic model of cholera disease spreading by quarantine is discussed. It is assumed that the spread of cholera not only through direct contact between susceptible human populations with bacteria but also through direct contact between susceptible human populations with infected human populations and reduced bacterial populations not only die naturally but can also be done by means of extermination bacteria. Determination of equilibrium points, existence and local stability of equilibrium points are investigated. Numerical simulations are performed to illustrate the results of the analysis. Keywords: Cholera Disease, Epidemic Model, Runge-Kutta Method 4th order, Stability, Quarantine.

Highlights

Cholera disease is a disease caused by drinking water contaminated by poor sanitation or food contaminated by Vibrio cholera bacteria
Cholera diseases can be transmitted by direct contact between susceptible populations and the bacterial populations present in the environment [1]
The SIQRB model is a modification of the model [1] by adding direct contact of susceptible human populations to infected human population and bacterial eradication in model [2]

Summary

INTRODUCTION

Cholera disease is a disease caused by drinking water contaminated by poor sanitation or food contaminated by Vibrio cholera bacteria. In addition cholera disease can be transmitted through direct contact between susceptible populations with infected individuals [2]. The method used to determine the spread of disease is by using mathematical model of disease epidemic. The model used to determine the spread of cholera disease is the SIRB model (Susceptible-Infected- Recovered -Bacterial) [2,6,7,8]. The SIRB model was developed into the SIQRB model (Susceptible, Infected, Quarantine, Recovered, Bacteria) by adding class Q (Quarantine) [1]. The cholera disease distribution model will be discussed using the SIQRB type model by modifying from model [1] by adding direct contact of susceptible and infected human populations and bacterial eradication in model [2]. A numerical simulation is performed to illustrate the results of the analysis with Runge-Kutta Method 4th order

MATERIALS AND METHODS

AND DISCUSSION Model Formulation

CONCLUSION