A Vaccination Model for Transmission Dynamics of Influenza

Alexander, Murray E.; Bowman, Christopher; Moghadas, Seyed M.; Summers, Randy; Gumel, Abba B.; Sahai, Beni M.

doi:10.1137/030600370

Cited by 150 publications

(103 citation statements)

References 36 publications

Supporting

Mentioning

101

Contrasting

Unclassified

Order By: Relevance

“…This is quite a positive point, since it is known that the use of an imperfect vaccine can sometimes result in detrimental consequences to the community [16,17]. Many vaccination models [1,4,16,26] possess multiple stable equilibria and exhibit phenomena such as backward and fold bifurcations, where the disease can still persist in the population even when the classical epidemiological requirement of R v < 1 is satisfied. The features that are thought to lead to these phenomena, in particular waning vaccine Overall, this study shows that a future SARS vaccine (assumed to be imperfect) that can make the control reproduction number less than unity will effectively control future SARS outbreaks in the community.…”

Section: 3mentioning

confidence: 99%

“…While in some of these studies (e.g., [3,6,16,17,37]) the vaccine is only given to people newly recruited into the population, such as newborns (cohort vaccination), in many others (e.g., in [1,20,26,35]), a proportion of susceptible individuals is continuously vaccinated. In other studies, such as Arino et al [4], both cohort and continuous vaccination are provided.…”

mentioning

confidence: 99%

“…Over the past few decades, a large number of simple compartmental mathematical models of the general form SVI or SVIR (where S, V, I and R denote the populations of susceptible, vaccinated, infectious and recovered individuals) have been used in the literature to assess the impact or potential impact of imperfect vaccines for combatting the spread of some human diseases (see, for instance, [1,3,4,6,16,17,18,20,24,25,26,35,37] and the references therein). While in some of these studies (e.g., [3,6,16,17,37]) the vaccine is only given to people newly recruited into the population, such as newborns (cohort vaccination), in many others (e.g., in [1,20,26,35]), a proportion of susceptible individuals is continuously vaccinated.…”

mentioning

confidence: 99%

See 2 more Smart Citations

An sveir model for assessing potential impact of an imperfect anti-SARS vaccine

Gumel

McCluskey

Watmough

2006

Mathematical Biosciences and Engineering

109

View full text Add to dashboard Cite

Abstract. The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease that spread to over 32 countries in 2003, was based on quarantine of latently infected individuals and isolation of individuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials of some candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine, assumed to be imperfect, in curtailing future outbreaks. A relatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamics of the model are determined by a certain threshold quantity known as the control reproduction number (Rv ). If Rv ≤ 1, the disease will be eliminated from the community; whereas an epidemic occurs if Rv > 1. This study further shows that an imperfect SARS vaccine with infection-blocking efficacy is always beneficial in reducing disease spread within the community, although its overall impact increases with increasing efficacy and coverage. In particular, it is shown that the fraction of individuals vaccinated at steady-state and vaccine efficacy play equal roles in reducing disease burden, and the vaccine must have efficacy of at least 75% to lead to effective control of SARS (assuming R 0 = 4). Numerical simulations are used to explore the severity of outbreaks when Rv > 1.

show abstract

Section: 3mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

An sveir model for assessing potential impact of an imperfect anti-SARS vaccine

Gumel

McCluskey

Watmough

2006

Mathematical Biosciences and Engineering

109

View full text Add to dashboard Cite

show abstract

“…Vaccines are considered the first line of defense against influenza to prevent infection and control the spread of the disease (USGAO 2007). Despite the availability of preventive vaccines and public health vaccination programs, influenza inflicts substantial morbidity, mortality, and socioeconomic costs and remains a major public health problem (Alexander et al 2004). This is largely because the protection conferred by current vaccines is dependent on the immune status of the individual, ranging between 70-90% in healthy young adults and 30-40% among the elderly and others with weakened immune systems (Alexander et al 2004).…”

Section: Introductionmentioning

confidence: 99%

Optimal Control and Sensitivity Analysis of an Influenza Model with Treatment and Vaccination

Khamis²,

et al. 2010

View full text Add to dashboard Cite

We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatment using two preventive scenarios: increase and decrease in vaccine uptake. Due to the seasonality of the influenza pandemic, the dynamics is studied in a finite time interval. We focus primarily on controlling the disease with a possible minimal cost and side effects using control theory which is therefore applied via the Pontryagin's maximum principle, and it is observed that full treatment effort should be given while increasing vaccination at the onset of the outbreak. Next, sensitivity analysis and simulations (using the fourth order Runge-Kutta scheme) are carried out in order to determine the relative importance of different factors responsible for disease transmission and prevalence. The most sensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive parameters for the endemic equilibrium point.

show abstract

“…Sehingga strategi vaksinasi kontinu pada model SVIRS ini berdasar pada model epidemik dasar untuk suatu penyakit yang tidak menyebabkan kematian (non fatal) serta berdasarkan pada Hethcote [6], Alexander et al [7] serta Xianning Liu [8] :…”

Section: Model Epidemik Svirs Dengan Strategi Vaksinasi Kontinuunclassified

Pengaruh Strategi Vaksinasi Kontinu Pada Model Epidemik SVIRS

Marentek¹

2017

Preprint

View full text Add to dashboard Cite

AbstrakPenyebaran penyakit menular sangat berbahaya sehingga perlu diminimalisir. Vaksinasi adalah salah satu cara untuk meminimalisir penyebaran penyakit menular ataupun untuk memberantas penyakit. Berdasarkan proses vaksinasi terdapat dua strategi vaksinasi yaitu strategi vaksinasi kontinu dan strategi vaksinasi terputus. Penelitian ini membahas strategi vaksinasi kontinu pada model epidemik SVIRS, dari hasil analisis diperoleh dua titik tetap yaitu titik tetap bebas penyakit dan tititk tetap endemik dan juga suatu nilai ambang batas epidemik yaitu bilangan reproduksi dasar yang selanjutnya digunakan sebagai batasan untuk analisis selanjutnya. Ambang batas epidemik atau bilangan reproduksi dasar sepenuhnya bergantung pada strategi vaksinasi kontinu yang dilakukan. Jika strategi vaksinasi yang dilakukan berada diatas atau sama dengan tingkat vaksinasi minimum maka titik tetap bebas penyakit akan stabil asimtotik yang artinya penyakit tidak akan menyebar dan pada akhirnya penyakit akan hilang dari populasi. Sebaliknya, jika strategi vaksinasi kontinu yang dilakukan berada dibawah tingkat vaksinasi minimum maka titik tetap endemik akan stabil asimtotik sehingga penyakit akan menyebar dan menjadi endemik. Selain itu dari hasil simuasi yang dilakukan dengan perangkat lunak Mathematica diperoleh bahwa vaksinasi berpengaruh dapat menurunkan proporsi individu yang terinfeksi dari populasi dan dengan strategi vaksinasi yang tepat yaitu strategi yang dilakukan lebih dari atau sama dengan tingkat vaksinasi minimum akan berhasil mencegah penyebaran penyakit menular.Kata Kunci: Model Epidemik, SVIR, Vaksinasi, Strategi, Kestabilan PENDAHULUANPenyebaran penyakit menular memiliki pengaruh yang luar biasa pada kehidupan manusia. Setiap tahun jutaan orang meninggal karena berbagai penyakit menular. Sehingga perlu dikendalikan atau diminimalisir agar tidak terjadi epidemik salah satu caranya dengan melakukan program vaksinasi. Sehingga untuk mengetahui seberapa besar laju penyebaran suatu penyakit menular secara matematis adalah dengan membuat model matematika penyebaran penyakit menular atau model matematika epidemik. Pertama, pola epidemik dapat digambarkan secara matematis dengan menghampiri keadaan sebenarnya. Kedua, menganalisa pola epidemik melalui model yang telah dirumuskan. Kemudian menginterpretasikan hasil analisa ke dalam keadaan sebenarnya.Vaksinasi adalah salah satu cara untuk mencegah atau meminimalisir penyebaran suatu penyakit menular. Dan kini vaksinasi rutin disediakan disemua negara-negara berkembang terhadap semua penyakit. Pemberantasan atau eradikasi penyakit cacar yang terakhir terlihat dalam kasus alami pada tahun 1977 telah dianggap sebagai keberhasilan paling spektakuler vaksinasi [1].

show abstract

A Vaccination Model for Transmission Dynamics of Influenza

Cited by 150 publications

References 36 publications

An sveir model for assessing potential impact of an imperfect anti-SARS vaccine

An sveir model for assessing potential impact of an imperfect anti-SARS vaccine

Optimal Control and Sensitivity Analysis of an Influenza Model with Treatment and Vaccination

Pengaruh Strategi Vaksinasi Kontinu Pada Model Epidemik SVIRS

Contact Info

Product

Resources

About