Modeling the effect of time delay in controlling the carrier dependent infectious disease – Cholera

Misra, Arvind; Mishra, S. N.; Pathak, Anagh; Misra, Peeyush; Naresh, Ram

doi:10.1016/j.amc.2012.04.085

Cited by 20 publications

(6 citation statements)

References 21 publications

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“…. ., then ± are a pair of purely imaginary roots of (23). This allows us to define the Hopf-bifurcation threshold time delay value as…”

Section: Delay Only In Seeking Medicalmentioning

confidence: 99%

“…Delays change the dynamical systems' stability by giving rise to Hopf-bifurcations [19,22]. Works done by researchers, for example, [8,[23][24][25][26], demonstrate the role played by time delays in different capacities in controlling the spread of infectious diseases. Sharma et al [27] discussed avian influenza transmission dynamics with two discrete time delays as incubation periods of avian influenza in the human and avian populations and found out that increment in time delays occurrence results into decrease in infected human population.…”

Section: Introductionmentioning

confidence: 99%

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Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Mbabazi¹,

Mugisha

Kimathi

2019

Abstract and Applied Analysis

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In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratioR0is less than unity and unstable otherwise. The stability of equilibria with delays shows that the endemic equilibrium is locally stable without delays and stable if the delays are under conditions. The existence of Hopf-bifurcation is investigated and transversality conditions are proved. The model results suggest that, as the respective delays exceed some critical value past the endemic equilibrium, the system loses stability through the process of local birth or death of oscillations. Further, a decrease or an increase in the delays leads to asymptotic stability or instability of the endemic equilibrium, respectively. The analytical results are supported by numerical simulations.

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“…. ., then ± are a pair of purely imaginary roots of (23). This allows us to define the Hopf-bifurcation threshold time delay value as…”

Section: Delay Only In Seeking Medicalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Mbabazi¹,

Mugisha

Kimathi

2019

Abstract and Applied Analysis

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“…One of the most important factors influencing the understanding and control of pandemics is some time delay of the process, when a certain time elapses from the moment of infection to the moment of active manifestation of the virus, after which the individual becomes a source of infection [5,6]. The effects of delay mask the causal relationships in the dynamics of SV, and make wrong any linear prediction, even in the short term.…”

Section: Introductionmentioning

confidence: 99%

Spread of infection with time-delay activation in a small world

Golovinski

2020

Preprint

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A model of the spread of viruses in a network of cities is considered, taking into account a delay caused by the long incubation period of the viruses. The usual infection spread and dynamics with a delay are compared. A temporary asymmetry of the infection spread has been identified, when the time of the pandemic developing significantly exceeds the time for its completion. Numerical simulations of the spread of viruses in a network of interconnected large and small cities were carried out, and pandemic features in a small world were revealed, including the possibility of re-infection of the megalopolises.

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“…6,7 However, later on, it has been recognized that these diseases also spread due to the carriers (eg, flies, insects or other entities) present in the environment, a fact commonly known as indirect transmission. 3,[7][8][9][10][11][12] Understanding the dynamics of food-borne diseases, such as typhoid fever, and so on, has been a major research task in the last few decades, the basic assumption on their spread only being the consumption of contaminated food. [13][14][15][16][17] Furthermore, in References 18,19, direct disease transmission is also considered in addition to indirect transmission (due to consumption of contaminated water).…”

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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Modeling the effect of time delay in controlling the carrier dependent infectious disease – Cholera

Cited by 20 publications

References 21 publications

Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Spread of infection with time-delay activation in a small world

Modeling biological control of carrier‐dependent infectious diseases

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