Modeling and Analysis of the Spread of an Infectious Disease Cholera with Environmental Fluctuations

Authors

Manju Agarwal, University of Lucknow
Vinay Verma, University of Lucknow

Abstract

A nonlinear delayed mathematical model with immigration for the spread of an infectious disease cholera with carriers in the environment is proposed and analyzed. It is assumed that all susceptible are affected by carrier population density. The carrier population density is assumed to follow the logistic model and grows due to conducive human population density related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free (DFE), (CFE) and endemic equilibria are found and their stability investigated. Bifurcation analyses about endemic equilibrium are also carried out analytically using the theory of differential equations. The model study shows that the spread of the infectious disease cholera increases due to growth of carriers in the environment and disease becomes more endemic due to immigration. Numerical simulations are also carried out to investigate the influence of certain parameters on the spread of disease, to support the analytical results of the model.

Recommended Citation

Agarwal, Manju and Verma, Vinay (2012). Modeling and Analysis of the Spread of an Infectious Disease Cholera with Environmental Fluctuations, Applications and Applied Mathematics: An International Journal (AAM), Vol. 7, Iss. 1, Article 27.
Available at: https://digitalcommons.pvamu.edu/aam/vol7/iss1/27