Impulsive Vaccination SEIR Model with Nonlinear Incidence Rate and Time Delay

This paper aims to discuss the delay epidemic model with vertical transmission, constant input, and nonlinear incidence. Some sufficient conditions are given to guarantee the existence and global attractiveness of the infection-free periodic solution and the uniform persistence of the addressed model with time delay. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results

Modelling and controlling infectious diseases

The financial support by IDRC has made it much easier to put together network activities involving scientists in both countries, a special example is the large presence of the Chinese students in the 2012 Summer School on Mathematics for Public Health the Canadian group organized in Edmonton in May of 2012.Infectious disease control is a major challenge in China due to China’s fast growing economy, changing social networks and evolving health service infrastructures. The success of disease control in China has a profound impact beyond its borders. In support of better disease control, this five year research program was designed to enhance China’s national capacity for analyzing, modeling and predicting transmission dynamics of infectious diseases through joint research, training young scientists, and building collaborative relationships. This successful program was led by the National Center for AIDS/STD Control and Prevention (Chinese Centre for Disease Control and Prevention, China) and the Centre for Disease Modeling (York University, Canada), and involved a number of Canadian and Chinese universities in various areas of infectious disease modelling and control. The bilateral collaboration also trained numerous highly qualified personnel and built a network for sustaining collaboration. This capacity building was facilitated by joint projects and bilateral annual meetings in major cities in China and Canada. The research activities on modeling major public health threats of infectious diseases focused on major diseases in China and/or issues of global public health concern including HIV transmission and prevention among high risk population, HIV treatment and drug resistance, influenza, schistosomiasis, mutation and stemma of SIV and HIV, latent and active tuberculosis infection, HBV control and vaccination. The outputs of the project were reported through peer-reviewed publications and modelling– based and science-informed public policy recommendations

Infectious Disease Modeling with Interpersonal Contact Patterns as a Heterogeneous Network

In this thesis, we study deterministic compartmental epidemic models. The conventional mass-mixing assumption is replaced with infectious disease contraction occurring within a heterogeneous network. Modeling infectious diseases with a heterogeneous contact network divides disease status compartments into further sub-compartments by degree class and thus allows for the finite set of contacts of an individual to play a role in disease transmission. These epidemiological network models are introduced as switched systems, which are systems that combine continuous dynamics with discrete logic. Many models are investi- gated, including SIS, SIR, SIRS, SEIR type models, and multi-city models. We analyze the stability of these switched network models. Particularly, we consider the transmission rate as a piecewise constant that changes value according to a switching signal. We establish threshold criteria for the eradication of a disease or stability of an endemic equilibrium using Lyapunov function techniques. Simulations are also conducted to support our claims and conclude conjectures. We test constant control and pulse control schemes, including vaccination, treatment, and screening processes for the application of these infectious disease models. Necessary critical control values are determined for the eradication of the disease

Infectious Disease Modeling with Interpersonal Contact Patterns as a Heterogeneous Network

In this thesis, we study deterministic compartmental epidemic models. The conventional mass-mixing assumption is replaced with infectious disease contraction occurring within a heterogeneous network. Modeling infectious diseases with a heterogeneous contact network divides disease status compartments into further sub-compartments by degree class and thus allows for the finite set of contacts of an individual to play a role in disease transmission. These epidemiological network models are introduced as switched systems, which are systems that combine continuous dynamics with discrete logic. Many models are investi- gated, including SIS, SIR, SIRS, SEIR type models, and multi-city models. We analyze the stability of these switched network models. Particularly, we consider the transmission rate as a piecewise constant that changes value according to a switching signal. We establish threshold criteria for the eradication of a disease or stability of an endemic equilibrium using Lyapunov function techniques. Simulations are also conducted to support our claims and conclude conjectures. We test constant control and pulse control schemes, including vaccination, treatment, and screening processes for the application of these infectious disease models. Necessary critical control values are determined for the eradication of the disease

A Study of Infectious Disease Models with Switching

Infectious disease models with switching are constructed and investigated in detail. Modelling infectious diseases as switched systems, which are systems that combine continuous dynamics with discrete logic, allows for the use of methods from switched systems theory. These methods are used to analyze the stability and long-term behaviour of the proposed switched epidemiological models. Switching is first incorporated into epidemiological models by assuming the contact rate to be time-dependent and better approximated by a piecewise constant. Epidemiological models with switched incidence rates are also investigated. Threshold criteria are established that are sufficient for the eradication of the disease, and, hence, the stability of the disease-free solution. In the case of an endemic disease, some criteria are developed that establish the persistence of the disease. Lyapunov function techniques, as well as techniques for stability of impulsive or non-impulsive switched systems with both stable and unstable modes are used. These methods are first applied to switched epidemiological models which are intrinsically one-dimensional. Multi-dimensional disease models with switching are then investigated in detail. An important part of studying epidemiology is to construct control strategies in order to eradicate a disease, which would otherwise be persistent. Hence, the application of controls schemes to switched epidemiological models are investigated. Finally, epidemiological models with switched general nonlinear incidence rates are considered. Simulations are given throughout to illustrate our results, as well as to make some conjectures. Some conclusions are made and future directions are given

Modelling the effect of mass media on influenza transmission and vaccine uptake

Influenza causes annual epidemics and occasional pandemics that have claimed millions of lives throughout history. Media reports affect social behaviour during epidemics and pandemics. Changes in social behaviour, in turn, effect key epidemic measurements such as peak magnitude, time to peak, and the beginning and end of an epidemic. The extent of this effect has not been realized. Mathematical models can be employed to study the effects of mass media. In this work, previous mathematical models concerning epidemics and mass media are studied. A novel inclusion of mass media is developed through the addition of a mass media compartment in a Susceptible-Exposed-Infected-Recovered (SEIR) model to look at the effect of mass media on an epidemic. Multiple levels of social distancing are considered in the framework of an ODE model. Vaccination is included in various models for susceptible individuals. Systems of stochastic differential equation models for each of the different scenarios have been derived. An Agent-Based Monte Carlo (ABMC) simulation is used to determine the variability in these key epidemic measurements, so as to provide some insight in to the effects of mass media on epidemic data. Data can help to provide an epidemic outcome that is seen at the population level. Data is used in order to inform parameter values and the novel inclusion of media. A look to future work is also included

Modeling and analyzing HIV transmission: the effect of contact patterns

A compartmental model is presented for the spread of HIV in a homosexual population divided into subgroups by degree of sexual activity. The model includes constant recruitment rates for the susceptibles in the subgroups. It incorporates the long infectious period of HIV-infected individuals and allows one to vary infectiousness over the infectious period. A new pattern of mixing, termed preferred mixing, is defined, in which a fraction of a group's contacts can be reserved for within-group contacts, the remainder being subject to proportional mixing. The fraction reserved may differ among groups. In addition, the classic definition of reproductive number is generalized to show that for heterogeneous populations in general the endemic threshold is [beta]DcY, where cY is the mean number of contacts per infective. The most important finding is that the pattern of contacts between the different groups has a major effect on the spread of HIV, an effect inadequately recognized or studied heretofore.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27021/1/0000009.pd

In-vivo dynamics of HIV-1 evolution

Ph. D, Faculty of Science, University of Witwatersrand, 2011The evolution of drug resistance in human immunodeficiency virus (HIV) infection has been a focus of research in many fields, as it continues to pose a problem to disease prevention and HIV patient management. In addition to techniques of molecular biology, studies in mathematical modelling have contributed to the knowledge here, but many questions remain unanswered. This thesis explores the application of a number of hybrid stochastic/deterministic models of viral replication to scenarios where viral evolution may be clinically or epidemiologically important. The choice of appropriate measures of viral evolution/diversity is non-trivial, and this impacts on the choice of mathematical techniques deployed. The use of probability generating functions to describe mutations occurring during early infection scenarios suggest that very early interventions such as pre-exposure prophylaxis (PrEP) or vaccines may substantially reduce viral diversity in cases of breakthrough infection. A modified survival analysis coupled to a deterministic model of viral replication during transient and chronic treatment helps identify clinically measurable indicators of the time it takes for deleterious rare mutations to appear. Lastly, persistence of problematic mutations is studied through the use of deterministic models with stochastic averaging over initial conditions

Washington University Senior Undergraduate Research Digest (WUURD), Spring 2018

From the Washington University Office of Undergraduate Research Digest (WUURD), Vol. 13, 05-01-2018. Published by the Office of Undergraduate Research. Joy Zalis Kiefer, Director of Undergraduate Research and Associate Dean in the College of Arts & Scienc

A Qualitative IPA of the Motivations of Retirees’ Transitions to ‘Retirement’ Social Identities and the Consequences on Retirement Adjustment Satisfaction

Retirement is a relatively new phenomenon in relation toshifting from being a privilege for the few to becoming anormative ‘third age’ of the life course. However, retirementrepresents one of the major life course transitions in late adultlife and associated with this transition is the question of howwell people adjust to retirement and the consequences of howwell people negotiate this adjustment on their sense of worthand well-being can be either negative or positive. This paperpresents a qualitative approach through Social Identity Theoryand Self-determination Theory to explore the underpinningmotivational processes of retirees in their transition to‘retirement’ social identities and the consequences onsatisfaction in retirement. Semi-structured interviews wereconducted with four white British participants includingthree males and one female ranging in age from sixty-fourto sixty-nine and having retired between fifteen months andfour years. An Interpretative Phenomenological Analysis ofthe transcribed interviews led to five main themes emerging,namely Strength of identity with working life; Significanceof non-work-related aspects of life; Psychologically preparingfor retirement; Process of shifting/adjusting to retirement;Meeting expectations of retirement. The study found thatretirement is not a formulaic process but people experienceadjusting to retirement differently based on their individualmotivations and resources for preparing for and facilitatingthe transition. The findings from the study has implicationsin relation to the provision of intervention in supportingindividuals psychologically preparing for retirement beyondfinancial planning along with those experiencing negativeconsequences in transitioning to retirement