Mathematical Tools for Understanding Infectious Disease Dynamics

Diekmann, Odo; Heesterbeek, Hans; Britton, Tom

doi:10.1515/9781400845620

Cited by 415 publications

(504 citation statements)

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“…Epidemic modeling has a history of researching, and mathematicians also put forward many epidemic models [2,3,18]. In the domain of complex networks, SIR model [26,27,28,29] is one of the most investigated and classical epidemic models.…”

Section: Standard Sir Modelmentioning

confidence: 99%

“…The basic conceptual tools in understanding the epidemic spreading and the related effective strategies for epidemic controlling should be the epidemiological models [17,18]. Among the numerous possible models, the most investigated and classical models are SI model [19,20], SIS model [21,22,23,24,25] and SIR model [26,27,28,29], which can approximately describe the spreading of real viruses such as HIV, encephalitis, influenza virus in biological networks; computer virus, trash mail in technological networks; and even gossip in social networks.…”

Section: Introductionmentioning

confidence: 99%

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Epidemic spreading with nonlinear infectivity in weighted scale-free networks

Chu

Zhang

Guan

et al. 2011

Physica A: Statistical Mechanics and its Applications

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Abstract. In this paper, we investigate the epidemic spreading for SIR model in weighted scale-free networks with nonlinear infectivity, where the transmission rate in our analytical model is weighted. Concretely, we introduce the infectivity exponent α and the weight exponent β into the analytical SIR model, then examine the combination effects of α and β on the epidemic threshold and phase transition. We show that one can adjust the values of α and β to rebuild the epidemic threshold to a finite value, and it is observed that the steady epidemic prevalence R grows in an exponential form in the early stage, then follows hierarchical dynamics. Furthermore, we find α is more sensitive than β in the transformation of the epidemic threshold and epidemic prevalence, which might deliver some useful information or new insights in the epidemic spreading and the correlative immunization schemes.

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Section: Standard Sir Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Epidemic spreading with nonlinear infectivity in weighted scale-free networks

Chu

Zhang

Guan

et al. 2011

Physica A: Statistical Mechanics and its Applications

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show abstract

“…The total human population, [12,13,14]. The equations for the human compartment are the following equation (1) and The total population of vector population,…”

Section: Effect Of Vaccination To the Transmission Model Of H1n1 Virusmentioning

confidence: 99%

“…If the real parts of all eigenvalues ) ( are negative then that equilibrium state is locally stable [7,8,9,11,12,13].…”

Section: International Journal Of Modeling Andmentioning

confidence: 99%

Effect of Vaccination to the Transmission Model of H1N1 Virus

Sungchasit¹,

Pongsumpun²

2018

IJMO

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“…The modelling of epidemics has been the object of a vast number of studies over the past century 1 . The desire to understand their mechanism has led to the formulation of models which make possible the simulation of events for which laboratory experiments cannot be conducted easily.…”

Section: Introductionmentioning

confidence: 99%