The role of vaccination in controlling the outbreak of infectious diseases: a mathematical approach

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Parsamanesh m.

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Journal Paper

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Journal: VACCINE RESEARCH Year:2018 | Volume:5 | Issue:1 Page(s): 32-40

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Information Journal Paper

Title

The role of vaccination in controlling the outbreak of infectious diseases: a mathematical approach

Author(s)

Parsamanesh m. | Issue Writer Certificate

Keywords

Dynamical system

Epidemilogical model

SIS model

Stability

Vaccine

Abstract

Introduction: Infectious diseases threaten the public health; hence understanding their propagation mechanisms may help to control them. Mathematical models are tools that can help the scientists to understand the pathogens’ propagations and can provide strategies for their control in future. Methods: Using mathematical theorems and MATLAB software, a continuous-time model known as susceptible-infected-susceptible (SIS) for transmission of infection in a population was described and the effects of a vaccination program based on this framework was investigated. Results: It was shown that the model had two equilibria: the infection-free equilibrium and the infected equilibrium. A specific threshold in terms of model parameters was obtained and then the existence of the equilibria and asymptotic Stability of the system were stated with respect to this threshold. The theoretical results were also verified numerically by providing several simulations. Conclusion: The results indicated the Stability of this model which emphasized that parameters such as restricting the immigration, reducing harmful contacts between the susceptible and the infected individuals, increasing awareness level of people, and most-importantly vaccination will reduce the basic reproduction number and help to control the disease. Moreover, a relation to calculate the minimum doses for vaccinating of the new-comers and the susceptible individuals, was obtained.

Cites

Modeling of the propagation of infectious diseases: mathematics and population

References

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APA: Copy

Parsamanesh, m.. (2018). The role of vaccination in controlling the outbreak of infectious diseases: a mathematical approach. VACCINE RESEARCH, 5(1), 32-40. SID. https://sid.ir/paper/344421/en

Vancouver: Copy

Parsamanesh m.. The role of vaccination in controlling the outbreak of infectious diseases: a mathematical approach. VACCINE RESEARCH[Internet]. 2018;5(1):32-40. Available from: https://sid.ir/paper/344421/en

IEEE: Copy

m. Parsamanesh, “The role of vaccination in controlling the outbreak of infectious diseases: a mathematical approach,” VACCINE RESEARCH, vol. 5, no. 1, pp. 32–40, 2018, [Online]. Available: https://sid.ir/paper/344421/en

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