A stochastic multi-scale model of HIV-1 transmission for decision-making: application to a MSM population.

BackgroundIn the absence of an effective vaccine against HIV-1, the scientific community is presented with the challenge of developing alternative methods to curb its spread. Due to the complexity of the disease, however, our ability to predict the impact of various prevention and treatment strategies is limited. While ART has been widely accepted as the gold standard of modern care, its timing is debated.ObjectivesTo evaluate the impact of medical interventions at the level of individuals on the spread of infection across the whole population. Specifically, we investigate the impact of ART initiation timing on HIV-1 spread in an MSM (Men who have Sex with Men) population.Design and methodsA stochastic multi-scale model of HIV-1 transmission that integrates within a single framework the in-host cellular dynamics and their outcomes, patient health states, and sexual contact networks. The model captures disease state and progression within individuals, and allows for simulation of therapeutic strategies.ResultsEarly ART initiation may substantially affect disease spread through a population.ConclusionsOur model provides a multi-scale, systems-based approach to evaluate the broader implications of therapeutic strategies

A stochastic SIR model with contact-tracing: large population limits and statistical inference

A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing information related to persons with whom they have had possibly infectious contacts. The population evolves through demographic, infection and detection processes, in a way that its temporal evolution is described by a stochastic Markov process, of which the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures. For adequate scalings of the demographic, infection and detection rates, it is shown to converge to the weak deterministic solution of a PDE system, as a parameter n, interpreted as the population size roughly speaking, becomes large. From the perspective of the analysis of infectious disease data, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relation of the model to the available data of the HIV epidemic in Cuba, in which country a contact-tracing detection system has been set up since 1986, is investigated and numerical applications are carried out

MATHEMATICAL MODELING OF COMMUNICABLE IMPORTED DISEASES SCREENING IN THE UNITED ARAB EMIRATES

The United Arab Emirates (UAE), as one of the countries with high numbers of expatriates in the world, is expected to face public health challenges. The reason for this situation is that the majority of those expatriates belong to regions where health issues are usually left behind. This may create the possibility of having imported communicable diseases. However, screening policy should be tested and adapted to protect the population from any imported communicable disease. This study aims at identifying an approach and method to deal with these imported diseases via a set of differential equations. The spread of a communicable disease is examined by taking in consideration the nature of the expatriates in the UAE. The population of expatriates is divided into high risk and low risk groups. The study concluded to the possibility of the persistence of the diseases under seven possible scenarios. Each of these scenarios represents the endemic level of the disease. To clarify the case simulations of two types of diseases are examined: HIV and Tuberculosis (TB). Keywords: Basic reproduction number, stability analysis, local sensitivity analysi

Why did HIV decline in Uganda?

Uganda is widely viewed as a public health success for curtailing its HIV/AIDS epidemic in the early 1990s. We investigate the factors contributing to this decline. We first build a model of HIV transmission. Calibration of the model indicates that reduced pre-marital sexual activity among young women is the most important factor in the decline in HIV. We next explore what led young women to change their behavior. We estimate that approximately one-third the reduction in HIV in this cohort and almost 20 percent of the overall HIV decline was due to a gender-targeted education policy.

Biomathematics of Chlamydia

Chlamydia trachomatis (C. trachomatis) related sexually transmitted infections are a major global public health concern. C. trachomatis afflict millions of men, women, and children worldwide and frequently result in serious medical diseases. In this thesis, mathematical modeling is applied in order to comprehend the dynamics of Chlamydia pathogens within host, their interactions with the immune systems, behavior in the presence of other pathogens, transmission dynamics in a human population, and the efficacy of control measures. The thesis begins with a brief introduction of the bacteria Chlamydia in Chapter 1. In Chapter 2, we give a brief detail of the mathematical modeling of infectious diseases, and its specific application to study the pathogen. In Chapter 3, a linear delay differential compartmental model is developed, and its special application is shown for a laboratory experiment conducted to study the intracellular development cycle of Chlamydia. The delay accounts for the time spent by bacteria in their various forms and for the time taken to go through the replication cycle. The mathematical model tracks the number of Chlamydia infected cells at each stage of the cell division cycle. Moreover, the formula for the final size of each compartment is derived. With initial conditions taken from the experiment, the model is fitted to results from the laboratory data. This simple linear model is capable of reflecting the outcomes of the laboratory experiment. In Chapter 4, at a population level, a novel mathematical model is introduced to study the dynamics of the co-infection between C. trachomatis, and herpes simplex virus (HSV). The concept of the model is based on the observation that in an individual simultaneously infected with both pathogens, the presence of HSV will make the Chlamydia persistent. In its persistent phase, Chlamydia is not replicating and is non-infectious. Important threshold parameters are obtained for the persistence of both infections. We prove global stability results for the disease-free and the boundary equilibria by applying the theory of asymptotically autonomous systems. Further, the model is calibrated to disease parameters to determine the population prevalence of both diseases and compare it with epidemiological findings. In Chapter 5, a compartmental maturity structured model is developed to investigate an optimal control problem for the treatment of chronic Chlamydia infection. The model takes into account the interaction of the pathogens with the immune system and its effects on the formation of persistent Chlamydia particles. As the system takes the form of a mixed ODE-PDE system, the results of the conventional form of Pontryagin’s maximal principle for ordinary differential equations are not suitable. For our purpose, we construct an optimal control problem for a general maturity compartmental model, and hence it consists of ordinary and partial differential equations, moreover, the boundary conditions are also nonlinear. For a fixed control, we verify the existence, uniqueness, and boundedness of the solutions. The system is numerically simulated for a variety of cost functions in order to calculate the optimal treatment for curing Chlamyida infection. We believe that since our findings were validated for a general model with maturity structure, they may be applied to any specific compartmental model that is compatible with the established system

Modelling HIV/AIDS epidemic in Nigeria

Nigeria is one of the countries most affected by the HIV/AIDS pandemic, third only to India and South Africa. With about 10% of the global HIV/AIDS cases estimated to be in the country, the public health and socio-economic implications are enormous. This thesis has two broad aims: the first is to develop statistical models which adequately describe the spatial distribution of the Nigerian HIV/AIDS epidemic and its associated ecological risk factors; the second, to develop models that could reconstruct the HIV incidence curve, obtain an estimate of the hidden HIV/AIDS population and a short term projection for AIDS incidence and a measure of precision of the estimates. To achieve these objectives, we first examined data from various sources and selected three sets of data based on national coverage and minimal reporting delay. The data sets are the outcome of the National HIV/AIDS Sentinel Surveillance Survey conducted in 1999, 2001, 2003 and 2005 by the Federal Ministry of Health; the outcome of the survey of 1057 health and laboratory facilities conducted by the Nigerian Institute of Medical Research in 2000; and case by case HIV screening data collected from an HIV/AIDS centre of excellence. A thorough review of methods used by WHO/UNAIDS to produce estimates of the Nigerian HIV/AIDS scenario was carried out. The Estimation and Projection Package (EPP) currently being used for modelling the epidemic partitions the population into at-risk, not-at-risk and infected sub-populations. It also requires some parameter input representing the force of infection and behaviour or high risk adjustment parameter. It may be difficult to precisely ascertain the size of these population groups and parameters in countries as large and diverse as Nigeria. Also, the accuracy of vital rates used in the EPP and Spectrum program is doubtful. Literature on ordinary back-calculation, nonparametric back-calculation, and modified back-calculation methods was reviewed in detail. Also, an indepth review of disease mapping techniques including multilevel models and geostatistical methods was conducted. The existence of spatial clusters was investigated using cluster analysis and some measure of spatial autocorrelation (Moran I and Geary c coefficients, semivariogram and kriging) applied to the National HIV/AIDS Surveillance data. Results revealed the existence of spatial clusters with significant positive spatial autocorrelation coefficients that tended to get stronger as the epidemic developed through time. GAM and local regression fit on the data revealed spatial trends on the north-south and east - west axis. Analysis of hierarchical, spatial and ecological factor effects on the geographical variation of HIV prevalence using variance component and spatial multilevel models was performed using restricted maximum likelihood implemented in R and empirical and full Bayesian methods in WinBUGS. Results confirmed significant spatial effects and some ecological factors were significant in explaining the variation. Also, variation due to various levels of aggregation was prominent. Estimates of cumulative HIV infection in Nigeria were obtained from both parametric and nonparametric back-calculation methods. Step and spline functions were assumed for the HIV infection curve in the parametric case. Parameter estimates obtained using 3-step and 4-step models were similar but the standard errors of these parameters were higher in the 4-step model. Estimates obtained using linear, quadratic, cubic and natural splines differed and also depended on the number and positions of the knots. Cumulative HIV infection estimates obtained using the step function models were comparable with those obtained using nonparametric back-calculation methods. Estimates from nonparametric back-calculation were obtained using the EMS algorithm. The modified nonparametric back-calculation method makes use of HIV data instead of the AIDS incidence data that are used in parametric and ordinary nonparametric back-calculation methods. In this approach, the hazard of undergoing HIV test is different for routine and symptom-related tests. The constant hazard of routine testing and the proportionality coefficient of symptom-related tests were estimated from the data and incorporated into the HIV induction distribution function. Estimates of HIV prevalence differ widely (about three times higher) from those obtained using parametric and ordinary nonparametric back-calculation methods. Nonparametric bootstrap procedure was used to obtain point-wise confidence interval and the uncertainty in estimating or predicting precisely the most recent incidence of AIDS or HIV infection was noticeable in the models but greater when AIDS data was used in the back-projection model. Analysis of case by case HIV screening data indicate that of 33349 patients who attended the HIV laboratory of a centre of excellence for the treatment of HIV/AIDS between October 2000 and August 2006, 7646 (23%) were HIV positive with females constituting about 61% of the positive cases. The bulk of infection was found in patients aged 15-49 years, about 86 percent of infected females and 78 percent of males were in this age group. Attendance at the laboratory and the proportion of HIV positive tests witnessed a remarkable increase when screening became free of charge. Logistic regression analysis indicated a 3-way interaction between time period, age and sex. Removing the effect of time by stratifying by time period left 2-way interactions between age and sex. A Correction factor for underreporting was ascertained by studying attendance at the laboratory facility over two time periods defined by the cost of HIV screening. Estimates of HIV prevalence obtained from corrected data using the modified nonparametric back-calculation are comparable with UN estimates obtained by a different method. The Nigerian HIV/AIDS pandemic is made up of multiple epidemics spatially located in different parts of the country with most of them having the potential of being sustained into the future given information on some risk factors. It is hoped that the findings of this research will be a ready tool in the hands of policy makers in the formulation of policy and design of programs to combat the epidemic in the country. Access to data on HIV/AIDS are highly restricted in the country and this hampers more in-depth modelling of the epidemic. Subject to data availability, we recommend that further work be done on the construction of stratification models based on sex, age and the geopolitical zones in order to estimate the infection intensity in each of the population groups. Uncertainties surrounding assumptions of infection intensity and incubation distribution can be minimized using Bayesian methods in back-projection

Projecting the Number of New AIDS Cases in the U.S.

This paper reviews the two leading methods used to project the number of AIDS cases: back calculation and extrapolation. These methods are assessed in light of key features of the HIV/AIDS epidemic and of data on the epidemic; they are also assessed in terms of the quality of the projections they yield. Our analysis shows that both methods have tended to overproject, often by sizable amounts, the number of AIDS cases in the U.S., especially among homosexual/bisexual males and users of blood and blood products. Our results provide no evidence that the use of AZT and other prophylaxis accounts for these projection errors. Rather, the overprojections appear to be mainly the result of a considerable reduction in the rate of new HIV infection among the gay community starting in 1983-85. A new method for projecting AIDS cases is proposed that exploits knowledge about the process generating AIDS cases and that incorporates readily available information about rates of new HIV infection. This method is far less sensitive to estimates of the incubation distribution than the method of back calculation and is shown, for the two transmission categories studied, to generate far more accurate AIDS case projections through 1990 than those based on the method of extrapolation. Relative to the method of extrapolation, this method projects 22,000 fewer new AIDS cases for 1995 (a 36 percent difference). This method also projects that intravenous drug users will replace homosexual/bisexual men as the dominant transmission category for AIDS