Estimation of infection rate in epidemic models with multiple populations

Dissertação para obtenção do Grau de Mestre em Matemática e Aplicações Especialização em Actuariado, Estatística e Investigação Operacional

Uma abordagem probabilística do número de reprodução básica em modelos epidemiológicos com aplicação na ferrugem do eucalipto

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Simulación de la propagación del malware: modelos continuos vs. modelos discretos

La gran mayoría de modelos matemáticos propuestos hasta la fecha para simular la propagación del malware están basados en el uso de ecuaciones diferenciales. Dichos modelos son analizados de manera crítica en este trabajo, determinando las principales deficiencias que presentan y planteando distintas alternativas para su subsanación. En este sentido, se estudia el uso de los autómatas celulares como nuevo paradigma en el que basar los modelos epidemiológicos, proponiendo una alternativa explícita basada en ellos a un reciente modelo continuo.

Towards an ontology for mathematical modeling with application to epidemiology

EMAp - Escola de Matemática Aplicada

Risk Estimates of Dengue in Travelers to Dengue Endemic Areas Using Mathematical Models

Dengue has emerged as a frequent problem in international travelers. The risk depends on destination, duration, and season of travel. However, data to quantify the true risk for travelers to acquire dengue are lacking. We used mathematical models to estimate the risk of nonimmune persons to acquire dengue when traveling to Singapore. From the force of infection, we calculated the risk of dengue dependent on duration of stay and season of arrival. Our data highlight that the risk for nonimmune travelers to acquire dengue in Singapore is substantial but varies greatly with seasons and epidemic cycles. For instance, for a traveler who stays in Singapore for 1 week during the high dengue season in 2005, the risk of acquiring dengue was 0.17%, but it was only 0.00423% during the low season in a nonepidemic year such as 2002. Risk estimates based on mathematical modeling will help the travel medicine provider give better evidence-based advice for travelers to dengue endemic countries.

Mathematical modelling of schistosomiasis japonica: comparison of control strategies in the People's Republic of China

We present the first mathematical model on the transmission dynamics of Schistosoma japonicum. The work extends Barbour's classic model of schistosome transmission. It allows for the mammalian host heterogeneity characteristic of the S. japonicum life cycle, and solves the problem of under-specification of Barbour's model by the use of Chinese data we are collecting on human-bovine transmission in the Poyang Lake area of Jiangxi Province in China. The model predicts that in the lake/marshland areas of the Yangtze River basin: (1) once-early mass chemotherapy of humans is little better than twice-yearly mass chemotherapy in reducing human prevalence. Depending on the heterogeneity of prevalence within the population, targeted treatment of high prevalence groups, with lower overall coverage, can be more effective than mass treatment with higher overall coverage. Treatment confers a short term benefit only, with prevalence rising to endemic levels once chemotherapy programs are stopped (2) depending on the relative contributions of bovines and humans, bovine treatment can benefit humans almost as much as human treatment. Like human treatment, bovine treatment confers a short-term benefit. A combination of human and bovine treatment will dramatically reduce human prevalence and maintains the reduction for a longer period of time than treatment of a single host, although human prevalence rises once treatment ceases; (3) assuming 75% coverage of bovines, a bovine vaccine which acts on worm fecundity must have about 75% efficacy to reduce the reproduction rate below one and ensure mid-term reduction and long-term elimination of the parasite. Such a vaccination program should be accompanied by an initial period of human treatment to instigate a short-term reduction in prevalence, following which the reduction is enhanced by vaccine effects; (4) if the bovine vaccine is only 45% efficacious (the level of current prototype vaccines) it will lower the endemic prevalence, but will not result in elimination. If it is accompanied by an initial period of human treatment and by a 45% improvement in human sanitation or a 30% reduction in contaminated water contact by humans, elimination is then possible. (C) 2002 Elsevier Science B.V. All rights reserved.

Epidemiology and strain characteristics of Echinococcus granulosus in the Benghazi area of eastern Libya

The incidence of surgically confirmed cystic echinococcosis in eastern Libya was estimated to be at least 4.2 cases/100,000, with significantly more female cases than male. The prevalences of infection with Echinococcus granulosus among 1087 sheep, 881 goats, 428 camels and 614 cattle from the same region, determined postmortem in abattoirs, were 20%, 3.4%, 13.6% and 11%, respectively. Infection in the livestock was age-dependent and, generally, the female animals were more often infected than the male. The measurements of rostellar hooks on protoscoleces collected from sheep and cattle were similar but significantly different from the corresponding measurements of parasites of human or camel origin. However, when a portion of the cytochrome c-oxidase subunit I (coxl) gene from each of 30 protoscolex samples from Libya (12 from cattle, three from humans, five from camels and 10 from sheep) was sequenced, the sequences were all found to be identical to that published for the common sheep strain of E. granulosus.

Participatory Surveillance and Mathematical Models in Epidemiologic Research: Successes and Challenges

Theoretical epidemiology aims to understand the dynamics of diseases in populations and communities. Biological and behavioral processes are abstracted into mathematical formulations which aim to reproduce epidemiological observations. In this thesis a new system for the self-reporting of syndromic data — Influenzanet — is introduced and assessed. The system is currently being extended to address greater challenges of monitoring the health and well-being of tropical communities.(...)

New tools for epidemiology: a space odyssey

Geographical Information Systems (GIS) facilitate access to epidemiological data through visualization and may be consulted for the development of mathematical models and analysis by spatial statistics. Variables such as land-cover, land-use, elevations, surface temperatures, rainfall etc. emanating from earth-observing satellites, complement GIS as this information allows the analysis of disease distribution based on environmental characteristics. The strength of this approach issues from the specific environmental requirements of those causative infectious agents, which depend on intermediate hosts for their transmission. The distribution of these diseases is restricted, both by the environmental requirements of their intermediate hosts/vectors and by the ambient temperature inside these hosts, which effectively govern the speed of maturation of the parasite. This paper discusses the current capabilities with regard to satellite data collection in terms of resolution (spatial, temporal and spectral) of the sensor instruments on board drawing attention to the utility of computer-based models of the Earth for epidemiological research. Virtual globes, available from Google and other commercial firms, are superior to conventional maps as they do not only show geographical and man-made features, but also allow instant import of data-sets of specific interest, e.g. environmental parameters, demographic information etc., from the Internet.

Resurgence of HIV infection among men who have sex with men in Switzerland: mathematical modelling study.

BACKGROUND: New HIV infections in men who have sex with men (MSM) have increased in Switzerland since 2000 despite combination antiretroviral therapy (cART). The objectives of this mathematical modelling study were: to describe the dynamics of the HIV epidemic in MSM in Switzerland using national data; to explore the effects of hypothetical prevention scenarios; and to conduct a multivariate sensitivity analysis. METHODOLOGY/PRINCIPAL FINDINGS: The model describes HIV transmission, progression and the effects of cART using differential equations. The model was fitted to Swiss HIV and AIDS surveillance data and twelve unknown parameters were estimated. Predicted numbers of diagnosed HIV infections and AIDS cases fitted the observed data well. By the end of 2010, an estimated 13.5% (95% CI 12.5, 14.6%) of all HIV-infected MSM were undiagnosed and accounted for 81.8% (95% CI 81.1, 82.4%) of new HIV infections. The transmission rate was at its lowest from 1995-1999, with a nadir of 46 incident HIV infections in 1999, but increased from 2000. The estimated number of new infections continued to increase to more than 250 in 2010, although the reproduction number was still below the epidemic threshold. Prevention scenarios included temporary reductions in risk behaviour, annual test and treat, and reduction in risk behaviour to levels observed earlier in the epidemic. These led to predicted reductions in new infections from 2 to 26% by 2020. Parameters related to disease progression and relative infectiousness at different HIV stages had the greatest influence on estimates of the net transmission rate. CONCLUSIONS/SIGNIFICANCE: The model outputs suggest that the increase in HIV transmission amongst MSM in Switzerland is the result of continuing risky sexual behaviour, particularly by those unaware of their infection status. Long term reductions in the incidence of HIV infection in MSM in Switzerland will require increased and sustained uptake of effective interventions.

Direct and indirect effects of screening for Chlamydia trachomatis on the prevention of pelvic inflammatory disease: a mathematical modeling study

BACKGROUND Pelvic inflammatory disease (PID) results from the ascending spread of microorganisms, including Chlamydia trachomatis, to the upper genital tract. Screening could improve outcomes by identifying and treating chlamydial infections before they progress to PID (direct effect) or by reducing chlamydia transmission (indirect effect). METHODS We developed a compartmental model that represents a hypothetical heterosexual population and explicitly incorporates progression from chlamydia to clinical PID. Chlamydia screening was introduced, with coverage increasing each year for 10 years. We estimated the separate contributions of the direct and indirect effects of screening on PID cases prevented per 100,000 women. We explored the influence of varying the time point at which clinical PID could occur and of increasing the risk of PID after repeated chlamydial infections. RESULTS The probability of PID at baseline was 3.1% by age 25 years. After 5 years, the intervention scenario had prevented 187 PID cases per 100,000 women and after 10 years 956 PID cases per 100,000 women. At the start of screening, most PID cases were prevented by the direct effect. The indirect effect produced a small net increase in PID cases, which was outweighed by the effect of reduced chlamydia transmission after 2.2 years. The later that progression to PID occurs, the greater the contribution of the direct effect. Increasing the risk of PID with repeated chlamydial infection increases the number of PID cases prevented by screening. CONCLUSIONS This study shows the separate roles of direct and indirect PID prevention and potential harms, which cannot be demonstrated in observational studies.

Potential Impact of Sexual Transmission on Ebola Virus Epidemiology: Sierra Leone as a Case Study.

BACKGROUND Sexual transmission of Ebola virus disease (EVD) 6 months after onset of symptoms has been recently documented, and Ebola virus RNA has been detected in semen of survivors up to 9 months after onset of symptoms. As countries affected by the 2013-2015 epidemic in West Africa, by far the largest to date, are declared free of Ebola virus disease (EVD), it remains unclear what threat is posed by rare sexual transmission events that could arise from survivors. METHODOLOGY/PRINCIPAL FINDINGS We devised a compartmental mathematical model that includes sexual transmission from convalescent survivors: a SEICR (susceptible-exposed-infectious-convalescent-recovered) transmission model. We fitted the model to weekly incidence of EVD cases from the 2014-2015 epidemic in Sierra Leone. Sensitivity analyses and Monte Carlo simulations showed that a 0.1% per sex act transmission probability and a 3-month convalescent period (the two key unknown parameters of sexual transmission) create very few additional cases, but would extend the epidemic by 83 days [95% CI: 68-98 days] (p < 0.0001) on average. Strikingly, a 6-month convalescent period extended the average epidemic by 540 days (95% CI: 508-572 days), doubling the current length, despite an insignificant rise in the number of new cases generated. CONCLUSIONS/SIGNIFICANCE Our results show that reductions in the per sex act transmission probability via abstinence and condom use should reduce the number of sporadic sexual transmission events, but will not significantly reduce the epidemic size and may only minimally shorten the length of time the public health community must maintain response preparedness. While the number of infectious survivors is expected to greatly decline over the coming months, our results show that transmission events may still be expected for quite some time as each event results in a new potential cluster of non-sexual transmission. Precise measurement of the convalescent period is thus important for planning ongoing surveillance efforts.

Mathematical and empirical examinations of some epidemiological procedures

In epidemiology literature, it is often required to investigate the relationships between means where the levels of experiment are actually monotone sets forming a partition on the range of sampling values. With this need, the analysis of these group means is generally performed using classical analysis of variance (ANOVA). However, this method has never been challenged. In this dissertation, we will formulate and present our examination of its validity. First, the classical assumptions of normality and constant variance are not always true. Second, under the null hypothesis of equal means, the test statistic for the classical ANOVA technique is still valid. Third, when the hypothesis of equal means is rejected, the classical analysis techniques for hypotheses of contrasts are not valid. Fourth, under the alternative hypothesis, we can show that the monotone property of levels leads to the conclusion that the means are monotone. Fifth, we propose an appropriate method for handing the data in this situation. ^

The epidemiology of antibiotic resistance in hospitals: Paradoxes and prescriptions

A simple mathematical model of bacterial transmission within a hospital was used to study the effects of measures to control nosocomial transmission of bacteria and reduce antimicrobial resistance in nosocomial pathogens. The model predicts that: (i) Use of an antibiotic for which resistance is not yet present in a hospital will be positively associated at the individual level (odds ratio) with carriage of bacteria resistant to other antibiotics, but negatively associated at the population level (prevalence). Thus inferences from individual risk factors can yield misleading conclusions about the effect of antibiotic use on resistance to another antibiotic. (ii) Nonspecific interventions that reduce transmission of all bacteria within a hospital will disproportionately reduce the prevalence of colonization with resistant bacteria. (iii) Changes in the prevalence of resistance after a successful intervention will occur on a time scale of weeks to months, considerably faster than in community-acquired infections. Moreover, resistance can decline rapidly in a hospital even if it does not carry a fitness cost. The predictions of the model are compared with those of other models and published data. The implications for resistance control and study design are discussed, along with the limitations and assumptions of the model.

Species determination of Brazilian mammals implicated in the epidemiology of rabies based on the control region of mitochondrial DNA

Identification of animals that are decomposing or have been run over or burnt and cannot be visually identified is a problem in the surveillance and control of infectious diseases. Many of these animals are wild and represent a valuable source of information for epidemiologic research as they may be carriers of an infectious agent. This article discusses the results obtained using a method for identifying mammals genetically by sequencing their mitochondrial DNA control region. Fourteen species were analyzed and identified. These included the main reservoirs and transmitters of rabies virus, namely, canids, chiroptera and primates. The results prove that this method of genetic identification is both efficient and simple and that it can be used in the surveillance of infectious diseases which includes mammals in their epidemiologic cycle, such as rabies.