Mathematical Theory of Control Systems Design

“…Let U = (t ≥ t 0 ) × R n , t 0 ∈ R + , and consider a twice continuously differentiable function, W. With reference to [26], the following theorem holds. Note that for (23),…”

Section: Stochastic Stability Of the Positive Equilibriummentioning

confidence: 99%

Qualitative Analysis of a Cholera Bacteriophage Model

Das

Mukherjee

2012

ISRN Biomathematics

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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 ofVibrio cholerae. Stability analysis and numerical simulations suggest that bacteriophage may contribute to lessening the severity of cholera epidemics by reducing the number ofVibrio choleraein 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.

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“…Therefore, in this case one can restrict oneself to finite mixtures of selectors when looking for a solution of problem (3). Clearly in order to have an exact solution of problem (3), it is sufficient to require the lower semicontinuity of the functional R(·) and the compactness of D 1 .…”

Section: Solvability Of the Optimal Control Problem And Sufficient CLmentioning

confidence: 99%

“…These questions were discussed in [1,2] and in many other works. A very good idea of the traditional control theory can be obtained from the monograph [3]. The basic instrument there is the dynamic programming approach.…”

Section: Introductionmentioning

confidence: 99%