Modeling the Cumulative Effect of Ecological Factors in the Habitat on the Spread of Tuberculosis

Naresh, Ram; Pandey, Surabhi; Shukla, J.B.

doi:10.1142/s1793524509000728

Cited by 8 publications

(4 citation statements)

References 12 publications

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“…Based on this in [4], authors formulated a model where variable human and bacteria populations are taken into account and it is concluded that due to bacteria in the environment, equilibrium level of the infective population increases. The global properties of a very general tuberculosis model with two differential infectivity is discussed in [5].…”

Section: Introductionmentioning

confidence: 99%

Mathematical modelling of TB with the effects of case detection and treatment

Athithan¹,

Ghosh²

2013

Int. J. Dynam. Control

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In this paper a non-linear mathematical model of tuberculosis with case detection and treatment is proposed and analyzed. The whole population under consideration is divided into four compartments e.g. susceptible, exposed, infected and Recovered to study the transmission dynamics of the tuberculosis. Based on the immunity level, susceptible individuals move to exposed class or directly to infected class once they come into contact with an infective. This has been incorporated through progression rate which could be fast or slow. The equilibria of the model and the basic reproduction number R 0 are computed. It is observed that the disease free equilibrium of the model is locally asymptotically stable when R 0 < 1. The model exhibits backward bifurcation under certain restriction on parameters, which gives rise to existence of multiple endemic equilibria for R 0 < 1. This suggests that an accurate estimation of parameters and the level of control measures are required to reduce the infection prevalence of TB in endemic region and just R 0 < 1 is not enough to eliminate the disease from the population. R 0 needs to be lowered much below one to confirm the global stability of the disease free equilibrium. Numerical simulation is performed to demonstrate the analytical results. It is found that the increase in the rate of case detection shifts the bacward bifurcation diagram towards right which leads to increase in the threshold value of R 0. It is also shown that the treatment is reducing the equilibrium level of infective

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Section: Introductionmentioning

confidence: 99%

Mathematical modelling of TB with the effects of case detection and treatment

Athithan¹,

Ghosh²

2013

Int. J. Dynam. Control

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“…In this paper we present a model for the disease situation in India, one of the countries in which the disease is endemic. This work is an extension of previous results, [3,15,18] and in particular of the work in progress [19], in that we account for the diagnostic system to be partioned into the public and private sectors, contrary to what was assumed in the earlier works.…”

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confidence: 87%

A TB model: Is disease eradication possible in India?

Pandey¹,

Venturino²

2017

MBE

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Tuberculosis (TB) is returning to be a worldwide global public health threat. It is estimated that 9.6 million cases occurred in 2014, of which just two-thirds notified to public health authorities. The "missing cases" constitute a severe challenge for TB transmission control. TB is a severe disease in India, while, worldwide, the WHO estimates that one third of the entire world population is infected. Nowadays, incidence estimation relies increasingly more on notifications of new cases from routine surveillance. There is an urgent need for better estimates of the load of TB, in high-burden settings. We developed a simple model of TB transmission dynamics, using a dynamical system model, consisting of six classes of individuals. It contains the current medical epidemiologists' understanding of the spread of the Mycobacterium tuberculosis in humans, which is substantiated by field observations at the district level in India. The model incorporates the treatment options provided by the public and private sectors in India. Mathematically, an interesting feature of the system is that it exhibits a backward, or subcritical, bifurcation. One of the results of the investigation shows that the discrepancy between the diagnosis rates of the public and private sector does not seem to be the cause of the endemicity of the disease, and, unfortunately, even if they reached 100% of correct diagnosis, this would not be enough to achieve disease eradication. Several other approaches have been attempted on the basis of this model to indicate possible strategies that may lead to disease eradication, but the rather sad conclusion is that they unfortunately do not appear viable in practice.

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“…The spread of tuberculosis model [50] is the system of four differential equations with respect to time along with four variables that can be denoted together as a quaternion number instead of four real numbers. This model needs the intelligent behavior and automated analysis of bacterial effect to reach equilibrium from different initial conditions.…”

Section: A Function Approximation Of Model For Spread Of Tuberculosismentioning

confidence: 99%

On the Root-Power Mean Aggregation Based Neuron in Quaternionic Domain

Kumar¹,

Tripathi²

2018

IJISA

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This paper illustrates the new structure of artificial neuron based on root-power means (RPM) for quaternionic-valued signals and also presented an efficient learning process of neural networks with quaternionic-valued root-power means neurons (ℍ-RPMN). The main aim of this neuron is to present the potential capability of a nonlinear aggregation operation on the quaternionic-valued signals in neuron cell. A wide spectrum of aggregation ability of RPM in between minima and maxima has a beautiful property of changing its degree of compensation in the natural way which emulates the various existing neuron models as its special cases. Further, the quaternionic resilient propagation algorithm (ℍ-RPROP) with error-dependent weight backtracking step significantly accelerates the training speed and exhibits better approximation accuracy. The wide spectrums of benchmark problems are considered to evaluate the performance of proposed quaternionic rootpower mean neuron with ℍ-RPROP learning algorithm.

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Modeling the Cumulative Effect of Ecological Factors in the Habitat on the Spread of Tuberculosis

Cited by 8 publications

References 12 publications

Mathematical modelling of TB with the effects of case detection and treatment

Mathematical modelling of TB with the effects of case detection and treatment

A TB model: Is disease eradication possible in India?

On the Root-Power Mean Aggregation Based Neuron in Quaternionic Domain

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