Dynamic phenomena arising from an extended Core Group model

In order to obtain a reasonably accurate model for the spread of a particular infectious disease through a population, it may be necessary for this model to possess some degree of structural complexity. Many such models have, in recent years, been found to exhibit a phenomenon known as backward bifurcation, which generally implies the existence of two subcritical endemic equilibria. It is often possible to refine these models yet further, and we investigate here the influence such a refinement may have on the dynamic behaviour of a system in the region of the parameter space near R0 = 1. We consider a natural extension to a so-called core group model for the spread of a sexually transmitted disease, arguing that this may in fact give rise to a more realistic model. From the deterministic viewpoint we study the possible shapes of the resulting bifurcation diagrams and the associated stability patterns. Stochastic versions of both the original and the extended models are also developed so that the probability of extinction and time to extinction may be examined, allowing us to gain further insights into the complex system dynamics near R0 = 1. A number of interesting phenomena are observed, for which heuristic explanations are provided

Age-structured models and optimal control in mathematical equidemiology: a survey

In this chapter we shall discuss the use of both optimal control theory and age-structured epidemic models in mathematical epidemiology. We use a very broad definition of optimal control, for example mathematical models for control by vaccination, as well as applications of optimal control theory. This is a wide area and we have had to be selective. In terms of applications a lot of the models which we present are applicable to the spread of common childhood diseases as that is an area in which age-structured models have been shown to fit data well and are most commonly applied in practice. This is because vaccination programs are often age-dependent targeting children of a given age and so they need age-structured models. The first section of this chapter discusses age-structured epidemic models including the question of optimal vaccination in them. 2 Then we move on to the optimal control in “stage-structured” (rather than age-structured) epidemic models, in which the individuals are grouped into susceptible, infected, and so on, depending on their relation to the epidemic. This gives a survey of how the ideas of optimal control theory, in particular the Maximum Principle and dynamic programming have been applied in the past to determine optimal control strategies for an epidemic, for example by immunization or removal of infected individuals. We finish this section with a few papers which apply optimal control theory to drug epidemics. We next survey some articles which give applications of optimal control to age-structured epidemic models. Much of this work concerns the existence and structure of optimal age-dependent vaccination strategies for common childhood diseases but we cover some other applications too. This is followed by a short section on spatial models used to determine optimal epidemic control policies. A brief summary and discussion conclude

The SIS epidemic model with Markovian switching

Population systems are often subject to environmental noise. Motivated by Takeuchi et al. (2006), we will discuss in this paper the effect of telegraph noise on the well-known SIS epidemic model. We establish the explicit solution of the stochastic SIS epidemic model, which is useful in performing computer simulations. We also establish the conditions for extinction and persistence for the stochastic SIS epidemic model and compare these with the corresponding conditions for the deterministic SIS epidemic model. We first prove these results for a two-state Markov chain and then generalise them to a finite state space Markov chain. Computer simulations based on the explicit solution and the Euler--Maruyama scheme are performed to illustrate our theory. We include a more realistic example using appropriate parameter values for the spread of Streptococcus pneumoniae in children

Parameter estimation for the stochastic SIS epidemic model

In this paper we estimate the parameters in the stochastic SIS epidemic model by using pseudo-maximum likelihood estimation (pseudo-MLE) and least squares estimation. We obtain the point estimators and 100(1 − α)% confidence intervals as well as 100(1 − α)% joint confidence regions by applying least squares techniques. The pseudo-MLEs have almost the same form as the least squares case. We also obtain the exact as well as the asymptotic 100(1 − α)% joint confidence regions for the pseudo-MLEs. Computer simulations are performed to illustrate our theory

Highly Variable Genomic Landscape of Endogenous Retroviruses in the C57BL/6J Inbred Strain, Depending on Individual Mouse, Gender, Organ Type, and Organ Location.

Transposable repetitive elements, named the "TREome," represent ~40% of the mouse genome. We postulate that the germ line genome undergoes temporal and spatial diversification into somatic genomes in conjunction with the TREome activity. C57BL/6J inbred mice were subjected to genomic landscape analyses using a TREome probe from murine leukemia virus-type endogenous retroviruses (MLV-ERVs). None shared the same MLV-ERV landscape within each comparison group: (1) sperm and 18 tissues from one mouse, (2) six brain compartments from two females, (3) spleen and thymus samples from four age groups, (4) three spatial tissue sets from two females, and (5) kidney and liver samples from three females and three males. Interestingly, males had more genomic MLV-ERV copies than females; moreover, only in the males, the kidneys had higher MLV-ERV copies than the livers. Perhaps, the mouse-, gender-, and tissue/cell-dependent MLV-ERV landscapes are linked to the individual-specific and dynamic phenotypes of the C57BL/6J inbred population

An improved optimistic three-stage model for the spread of HIV amongst injecting intravenous drug users

We start off this paper with a brief introduction to modeling Human Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS) amongst sharing, injecting drug users (IDUs). Then we describe the mathematical model which we shall use which extends an existing model of the spread of HIV and AIDS amongst IDUs by incorporating loss of HIV infectivity over time. This is followed by the derivation of a key epidemiological parameter, the basic reproduction number R0. Next we give some analytical equilibrium, local and global stability results. We show that if R0 &gte 1 then the disease will always die out. For R0 > 1 there is the disease-free equilibrium (DFE) and a unique endemic equilibrium. The DFE is unstable. An approximation argument shows that we expect the endemic equilibrium to be locally stable. We next discuss a more realistic version of the model, relaxing the assumption that the number of addicts remains constant and obtain some results for this model. The subsequent section gives simulations for both models confirming that if R0 &gte 1 then the disease will die out and if R0 > 1 then if it is initially present the disease will tend to the unique endemic equilibrium. The simulation results are compared with the original model with no loss of HIV infectivity. Next the implications of these results for control strategies are considered. A brief summary concludes the paper

Swimming against the tide: a study of a neighbourhood trying to rediscover its ‘reason for being’– the case of South Bank, Redcar and Cleveland

Many of the programmes and initiatives to regenerate deprived neighbourhoods appear to have had limited lasting impact. It has been argued that one reason for this is that we still have little real understanding of the nature and scale of the problems some communities face (Bernt, 2009). This paper attempts to add to our knowledge through close study of an area with multiple problems and a history of failed regeneration attempts. An in-depth case study undertaken to explore the current situation and future prospects of South Bank, a small neighbourhood in the North East of England, highlights transferable knowledge which may be applied to other regeneration areas. The analysis considers the nature and consequences of industrial decline; entrenched deprivation; the stigmatization of communities; the value of community consultation and the potential impact of retail-led regeneration. We question whether negative stigma attached to places can be changed and we ask what the future may hold for deprived communities now that public sector funding has largely dried up, and we consider an alternative approach: the potential impacts of private sector retail-led regeneration in the absence of public sector funding

Mathematical modelling of internal HIV dynamics

We study a mathematical model for the viral dynamics of HIV in an infected individual in the presence of HAART. The paper starts with a literature review and then formulates the basic mathematical model. An expression for R0, the basic reproduction number of the virus under steady state application of HAART, is derived followed by an equilibrium and stability analysis. There is always a disease-free equilibrium (DFE) which is globally asymptotically stable for R0 1 then some simulations will die out whereas others will not. Stochastic simulations suggest that if R0 > 1 those which do not die out approach a stochastic quasi-equilibrium consisting of random uctuations about the non-trivial deterministic equilibrium levels, but the amplitude of these uctuations is so small that practically the system is at the non-trivial equilibrium. A brief discussion concludes the paper

'It'll get worse before it gets better': Local experiences of living in a regeneration area

The negative consequences of living in deprived neighbourhoods for residents’ quality of life are well documented. Area-based regeneration initiatives are invariably concerned with improving local quality of life over the long term. The process of regeneration, however, can itself directly result in immediate and potentially lasting negative effects for local communities. This paper discusses some of the ways in which living in an area undergoing regeneration can adversely affect inhabitants’ quality of life, including problems associated with voids, relocation, demolitions, environmental quality, complexity, funding issues, uncertainty, frustration, fear for the future and consultation fatigue. A case study approach draws examples from a deprived neighbourhood in the North East of England. The conclusion discusses some of the possible implications for future regeneration policy, including: the importance of ongoing communication between professionals and communities; the need to value local people’s experience, judgement and the contribution they can make to local decision-making processes; recognition that successful regeneration can take many years; and the implications of current UK government policy