Analysis of a Vaccination Model for Carrier Dependent Infectious Diseases with Environmental Effects

Naresh, Ram; Pandey, Surabhi; Misra, Arvind

doi:10.15388/na.2008.13.3.14561

Cited by 30 publications

(21 citation statements)

References 24 publications

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“…In [21] and [23] time-varying epidemic models are considered which take into account the loss of immunity of newborns, the mortality due to the disease and the possible presence of external infected populations. In [25], carrier-dependent infectious diseases (like cholera, measles etc.) are considered.…”

Section: Introduction Brief Description Of Some Previous Background mentioning

confidence: 99%

Feedback linearization-based vaccination control strategies for true-mass action type SEIR epidemic models

Sen¹,

Ibeas²,

Alonso‐Quesada³

2011

NAMC

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This paper presents a feedback linearization-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among susceptible and infected. The control objective is novel in the sense that the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously the remaining population (i.e. susceptible plus infected plus infectious) to asymptotically converge to zero. The vaccination policy is firstly designed on the above proposed tracking objective. Then, it is proven that identical vaccination rules might be found based on a general feedback linearization technique. Such a formal technique is very useful in control theory which provides a general method to generate families of vaccination policies with sound technical background which include those proposed in the former sections of the paper. The output zero dynamics of the normal canonical form in the theoretical feedback linearization analysis is identified with that of the removed-by-immunity population. The various proposed vaccination feedback rules involved one of more of the partial populations and there is a certain flexibility in their designs since some control parameters being multiplicative coefficients of the various populations may be zeroed. The basic properties of stability and positivity of the solutions are investigated in a joint way. The equilibrium points and their stability properties as well as the positivity of the solutions are also investigated.

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Section: Introduction Brief Description Of Some Previous Background mentioning

confidence: 99%

Feedback linearization-based vaccination control strategies for true-mass action type SEIR epidemic models

Sen¹,

Ibeas²,

Alonso‐Quesada³

2011

NAMC

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“…This has been totally successful for some diseases such as Smallpox, polio, measles, etc... [3]. Mathematical models that incorporate vaccination as a control measure have been used to drive some strategies, and to determine changes in qualitative behavior that could result from such a control measure [3,22,26,27]. A vaccine may fail to confer any protection in a proportion of vaccinees.…”

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confidence: 99%

“…In this case, the vaccine is not totally effective and vaccinated individuals can be directly infected [7]. When these aspect are included in the model, a rich dynamical behavior may arise including bi-stability, backward and forward bifurcation [3,13,22].…”

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confidence: 99%

“…Several studies used the mathematical models for hepatitis B with carriers to discuss the effects of vaccination on HBV transmission [11,21,26,27]. Others studies using large-scale computational models with carriers are aimed at other diseases [9,22,23]. More recently, a model in [16] was proposed to analyze the effects of carriers on the transmission dynamics of diseases.…”

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Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers

Manyombe

Mbang²,

Lubuma³

et al. 2016

MBE

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In this paper, an epidemic model is investigated for infectious diseases that can be transmitted through both the infectious individuals and the asymptomatic carriers (i.e., infected individuals who are contagious but do not show any disease symptoms). We propose a dose-structured vaccination model with multiple transmission pathways. Based on the range of the explicitly computed basic reproduction number, we prove the global stability of the disease-free when this threshold number is less or equal to the unity. Moreover, whenever it is greater than one, the existence of the unique endemic equilibrium is shown and its global stability is established for the case where the changes of displaying the disease symptoms are independent of the vulnerable classes. Further, the model is shown to exhibit a transcritical bifurcation with the unit basic reproduction number being the bifurcation parameter. The impacts of the asymptomatic carriers and the effectiveness of vaccination on the disease transmission are discussed through through the local and the global sensitivity analyses of the basic reproduction number. Finally, a case study of hepatitis B virus disease (HBV) is considered, with the numerical simulations presented to support the analytical results. They further suggest that, in high HBV prevalence countries, the combination of effective vaccination (i.e. ≥ 3 doses of HepB vaccine), the diagnosis of asymptomatic carriers and the treatment of symptomatic carriers may have a much greater positive impact on the disease control.

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“…During the disease transmission process, the spread of an infectious disease depends mainly on the interactions between susceptible and infected individuals. However, there are many other factors, such as media coverage, vaccinations, and migration of population, which also influence the spread of an infectious disease [31][32][33]. In particular, media coverage has a great impact on individual behavior towards the disease, and further affects the government health care interventions to control the spread of such disease.…”

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Impact of media coverage on epidemic spreading in complex networks

Wang

Cao

Zhou

et al. 2013

Physica A: Statistical Mechanics and its Applications

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h i g h l i g h t s• A new SIS network model obtained by introducing an information variable is proposed. • The diseases can be controlled through high efficiency of implementation.• The introduced parameters have significant impact on the final prevalence density.• The results may suggest effective control strategies incorporating media coverage. a b s t r a c t An SIS network model incorporating the influence of media coverage on transmission rate is formulated and analyzed. We calculate the basic reproduction number R 0 by utilizing the local stability of the disease-free equilibrium. Our results show that the disease-free equilibrium is globally asymptotically stable and that the disease dies out if R 0 is below 1; otherwise, the disease will persist and converge to a unique positive stationary state. This result may suggest effective control strategies to prevent disease through media coverage and education activities in finite-size scale-free networks. Numerical simulations are also performed to illustrate our results and to give more insights into the dynamical process.

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Analysis of a Vaccination Model for Carrier Dependent Infectious Diseases with Environmental Effects

Cited by 30 publications

References 24 publications

Feedback linearization-based vaccination control strategies for true-mass action type SEIR epidemic models

Feedback linearization-based vaccination control strategies for true-mass action type SEIR epidemic models

Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers

Impact of media coverage on epidemic spreading in complex networks

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