Qualitative Analysis of a Cholera Bacteriophage Model

Abstract

<jats:p>Cholera still remains as a severe global threat and is currently spreading in Africa and other parts of the world. The role of lytic bacteriophage as an intervention of cholera outbreaks is investigated using a mathematical model. Dynamics of cholera is discussed on basis of the basic reproduction number . Conditions of Hopf bifurcation are also derived for a positive net growth rate of<jats:italic>Vibrio cholerae</jats:italic>. Stability analysis and numerical simulations suggest that bacteriophage may contribute to lessening the severity of cholera epidemics by reducing the number of<jats:italic>Vibrio cholerae</jats:italic>in the environment. Hence with the presence of phage virus, cholera is self-limiting in nature. By using phage as a biological control agent in endemic areas, one may also influence the temporal dynamics of cholera epidemics while reducing the excessive use of chemicals. We also performed stochastic analysis which suggests that the model system is globally asymptotically stable in probability when the strengths of white noise are less than some specific quantities.</jats:p>

Computational Modelling of Cholera Bacteriophage with Treatment

“…A nonlinear mathematical model has been analysed to study the effect of bacteriophage and treatment in the environment while the cholera epidemic is in progress. This study is the extended work done by [6]. Qualitative analysis of the model shows that the model has two equilibrium points, the disease-free equilibrium and endemic equilibrium points.…”

“…The disease-free equilibrium point 0 E is globally asymptotically stable if 1 e R < when all solutions of system (1) which starts in 6 R + are bounded.…”

“…Bacteriophage might be useful as a research tool [4] [5] developed a model which accounted for the role played by Hiperinfectivity Vibrios in causing the cholera epidemic. A mathematical model by [6] was analysed to study the dynamics of cholera in terms of interaction between Vibrio cholerae and bacteriophage model.. However, in all the above studies, none of them incorporated the treatment.…”

Deterministic and stochastic analysis of an eco-epidemiological model

“…In the last equation when there is no prey, predator population suffers a natural death at the rate d. In the second term, b represents the conversion efficiency of the predator. Our model is also applicable to propagation of other disease like tuberculosis in livestock [34], avian influenza [35], vibrio cholerae [36,37], viral hepatitis A [38], etc. Biological significance and units of the model parameters are given in Table 1.…”

Assessing the Impact of Increasing Antimicrobial Resistance of Vibrio cholerae on the Future Trends of Cholera Epidemic

“…A brief survey on previous studies provides the context of this paper. Various theoretical studies have been carried out on mathematical modeling of cholera transmission dynamics, focusing on a number of different issues, see [6][7][8][9][10][11], to mention a few. King et al (2008) [11] proposed a two-path cholera model including a class for severe infections as well as a class for mild or inapparent infections.…”