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A singular perturbation approach to epidemics of vectortransmitted diseases

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Infectious Disease Modelling 2019年第1期4卷 115-123页

作者： fred brauer University of British Columbia Vancouver BCCanada

In vector-borne epidemic models there is often a substantial difference between the vector and host time *** makes it possible to use the quasi-steady-state to obtain final size relations.

关键词： perturbation singular quasi

Mathematical epidemiology:Past,present,and future

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Infectious Disease Modelling 2017年第2期2卷 113-127页

作者： fred brauer University of British Columbia VancouverBCCanada

We give a brief outline of some of the important aspects of the development of mathematical epidemiology.

关键词： Mathematical epidemiology brief

General Compartmental Epidemic Models

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Chinese Annals of Mathematics,Series B 2010年第3期31卷 289-304页

作者： fred brauer Department of Mathematics University of British Columbia

The age of infection approach introduced by Kermack and Mckendrick in 1927 gives a unified way of describing and analyzing a variety of epidemic models, including models with multiple stages, treatment, and heterogeneous mixing. The author gives a description of the main results for such models, emphasizing the use of the final size relation to estimate the size of the epidemic.

关键词：流行病模型隔室大小关系估计

Modelling and simulating Chikungunya spread with an unstructured triangular cellular automata

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Infectious Disease Modelling 2020年第1期5卷 197-220页

作者： Gerardo Ortigoza fred brauer Iris Neri Facultad de Ingeniería Universidad VeracruzanaBoca Del RíoVerMexico Mathematics Department University of British ColumbiaVancouverB.CCanada Maestría en Gestion Integrada de Cuencas Universidad Autonoma de QueretaroMexico

In this work we propose a mathematical model to simulate Chikungunya spread;the spread model is implemented in a C++ cellular automata code defined on unstructured triangular grids and space visualizations are performed with *** order to simulate the time space spread of the Chikungunya diseases we include assumptions such as:heterogeneous human and vector densities,population mobility,geographically localized points of infection using geographical information systems,changes in the probabilities of infection,extrinsic incubation and mosquito death rate due to environmental *** experiments reproduce the qualitative behavior of diseases spread and provide an insight to develop strategies to prevent the diseases spread.

关键词： Cellular automata Unstructured triangular grids Chikungunya spread

Some models for epidemics of vector-transmitted diseases

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Infectious Disease Modelling 2016年第1期1卷 79-87页

作者： fred brauer Carlos Castillo-Chavez Anuj Mubayi Sherry Towers University of British Columbia VancouverBCCanada Arizona State University TempeAZUSA

Vector-transmitted diseases such as dengue fever and chikungunya have been spreading rapidly in many parts of the *** Zika virus has been known since 1947 and invaded South America in *** can be transmitted not only by(mosquito)vectors but also directly through sexual *** has developed into a serious global health problem because,while most cases are asymptomatic or very light,babies born to Zika-infected mothers may develop microcephaly and other very serious birth *** formulate and analyze two epidemic models for vector-transmitted diseases,one appropriate for dengue and chikungunya fever outbreaks and one that includes direct transmission appropriate for Zika virus *** is especially important because the Zika virus is the first example of a disease that can be spread both indirectly through a vector and directly(through sexual contact).In both cases,we obtain expressions for the basic reproduction number and show how to use the initial exponential growth rate to estimate the basic reproduction ***,for the model that includes direct transmission some additional data would be needed to identify the fraction of cases transmitted *** for the 2015 Zika virus outbreak in Barranquilla,Colombia has been used to fit parameters to the model developed here and to estimate the basic reproduction number.

关键词： diseases mother epidemic

A co-interaction model of HIV and syphilis infection among gay,bisexual and other men who have sex with men

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Infectious Disease Modelling 2020年第1期5卷 855-870页

作者： Jummy Funke David Viviane Dias Lima Jielin Zhu fred brauer Department of Mathematics University of British ColumbiaVancouverBCV6T 1Z2Canada British Columbia Centre for Excellence in HIV/AIDS St.Paul’s HospitalVancouverBCV6Z 1Y6Canada Department of Interdisciplinary Studies University of British ColumbiaVancouverBCV6T 1Z4Canada Department of Medicine Faculty of MedicineUniversity of British ColumbiaVancouverBCV6T 1Z3Canada

We developed a mathematical model to study the co-interaction of HIV and syphilis infection among gay,bisexual and other men who have sex with men(gbMSM).We qualitatively analysed the model and established necessary conditions under which disease-free and endemic equilibria are asymptotically *** gave analytical expressions for the reproduction number,and showed that whenever the reproduction numbers of sub-models and co-interaction model are less than unity,the epidemics die out,while epidemics persist when they are greater than *** presented numerical simulations of the full model and showed qualitative changes of the dynamics of the full model to changes in the transmission *** numerical simulations using a set of reasonable parameter values showed that:(a)both diseases die out or co-exist whenever their reproduction number is less than or exceed unity.(b)HIV infection impacts syphilis prevalence negatively and vice versa.(c)one possibility of lowering the co-infection of HIV and syphilis among gbMSM is to increase both testing and treatment rates for syphilis and HIV infection,and decrease the rate at which HIV infected individuals go off treatment.

关键词： HIV Syphilis Mathematical model gbMSM Reproduction number Testing and treatment Stability