A mathematical model for the control of carrier-dependent infectious diseases with direct transmission and time delay

Misra, Arvind; Mishra, S. N.; Pathak, Anagh; Srivastava, Prashant K.; Chandra, Peeyush

doi:10.1016/j.chaos.2013.08.002

Cited by 15 publications

(4 citation statements)

References 22 publications

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“…In this section, we conduct simulation analysis of the model (3.1) to study its dynamical behavior and to prove the feasibility of local and nonlinear stability conditions of the model system. The numerical simulation of the system (3.1) is done by MAPLE 7.0 using the parameters values [8,9,11,15] given below: Since all the eigen values are negative which implies that the endemic equilibrium W3 is locally asymptotically stable.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…Mathematical models for the spread of infectious diseases have played a major role in providing deeper insight into the understanding of the transmission as well as control strategies [7,8,9,11,12,16,17], including HIV-TB co-infection [15]. For example, Feng et al [7] formulated a two strain TB model with an arbitrary distributed delay in the latent stage of individual infected with the drug-sensitive strain and investigated the effects of variable periods of latency on the disease dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Modeling the Effect of Ecological Conditions in the Habitat on the Spread of Tuberculosis

Mishra¹

2020

jnanabha

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In this paper, the cumulative effect of ecological conditions in the habitat on the spread of TB in human population is modeled and analyzed. The total human population is divided into two classes, susceptibles and infectives where the infective class is further subdivided into latent and actively infected subclasses. It is assumed that TB is spread by direct contact between members of the population as well as indirectly by bacteria which are emitted by infectives in the environment, survive and get accumulated due to favorable ecological conditions in the habitat. The cumulative density of ecological factors determining conditions in the habitat is assumed to follow a population density dependent logistic model. The analysis of the model shows that as parameters governing the ecological factors in the habitat increase, the spread of TB increases. The same result is also found with the increase in the parameter defining the accumulation of bacteria in the habitat. It is further found that due to immigration of the population TB becomes more endemic. A numerical study of the model is also carried out to see the role of key parameters on the spread of tuberculosis and to support the analytical results.

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Section: Numerical Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling the Effect of Ecological Conditions in the Habitat on the Spread of Tuberculosis

Mishra¹

2020

jnanabha

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“…Since the frequent outbreak of cholera brought the local public health a heavy burden, how to prevent and intervene cholera is particularly important. Common intervention methods of cholera include rehydration therapy, antibiotics, vaccination and water treatment [3,13,28,29,30,38,46]. In terms of reducing vibrio cholerae in the environment, Misra et al [30] introduced a delay SIRS-B compartment model to simulate the transmission of water-born disease, and discussed the effects of disinfectants on the control of diseases.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a partially degenerate reaction-diffusion cholera model with horizontal transmission and phage-bacteria interaction

Hu¹,

Wang²,

Nie³

2023

ejde

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We propose a cholera model with coupled reaction-diffusion equations and ordinary differential equations for discussing the effects of spatial heterogeneity, horizontal transmission, environmental viruses and phages on the spread of vibrio cholerae. We establish the well-posedness of this model which includes the existence of unique global positive solution, asymptotic smoothness of semiflow, and existence of a global attractor. The basic reproduction number R0 is obtained to describe the persistence and extinction of the disease. That is, the disease-free steady state is globally asymptotically stable for R0≤1, while it is unstable for R0>1. And, the disease is persistence and the model has the phage-free and phage-present endemic steady states in this case. Further, the global asymptotic stability of phage-free and phage-present endemic steady states are discussed for spatially homogeneous model. Finally, some numerical examples are displayed in order to illustrate the main theoretical results and our opening questions.

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“…[24][25][26][27][28] However, some of these measures could be harmful to the nontarget populations and/or have nonnegligible costs. 29 For these reasons, the use of biological agents has been advocated. 22,[30][31][32] An optimal control problem for carrier-dependent diseases is also investigated.…”

Section: Introductionmentioning

confidence: 99%

Modeling biological control of carrier‐dependent infectious diseases

Misra

Gupta

Venturino

2020

Comp and Math Methods

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Since decades, hazardous chemicals are used to control the growth of carriers (flies, ticks, mites, and so on) in the environment, which are responsible for the spread of many infectious diseases, such as typhoid fever, polio, and some skin infections such as leprosy, and so on. Although these chemicals reduce the carrier population, they also inflict a sizeable harm to nontarget populations, like the human population. In this study, we present a mathematical model to control the carrier population using biological agents, which leads to the control of carrier-dependent infectious diseases. It is assumed that the disease can spread in the human population due to the direct contact between susceptible and infected individuals, but also indirectly through the vector population. The feasibility and stability of the system's equilibria are discussed. The key parameters of the proposed model are identified and their role in the transmission and control of such diseases is discussed. Our findings show that combined actions of two strategies, the biological control of carriers via parasitic wasps that target the immature stage of the flies and any extra exogenous means which eradicate the adult carriers when their population is at low levels, could be an effective and low cost approach to lessen the disease propagation.

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A mathematical model for the control of carrier-dependent infectious diseases with direct transmission and time delay

Cited by 15 publications

References 22 publications

Modeling the Effect of Ecological Conditions in the Habitat on the Spread of Tuberculosis

Modeling the Effect of Ecological Conditions in the Habitat on the Spread of Tuberculosis

Dynamics of a partially degenerate reaction-diffusion cholera model with horizontal transmission and phage-bacteria interaction

Modeling biological control of carrier‐dependent infectious diseases

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