Statistical method for testing the neutral mutation hypothesis by DNA polymorphism.

Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.

https://epubs.siam.org/doi/pdf/10.1137/S0036144500371907

The Mathematics of Infectious Diseases

Summary Background Since December, 2019, Wuhan, China, has experienced an outbreak of coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epidemiological and clinical characteristics of patients with COVID-19 have been reported but risk factors for mortality and a detailed clinical course of illness, including viral shedding, have not been well described. Methods In this retrospective, multicentre cohort study, we included all adult inpatients (≥18 years old) with laboratory-confirmed COVID-19 from Jinyintan Hospital and Wuhan Pulmonary Hospital (Wuhan, China) who had been discharged or had died by Jan 31, 2020. Demographic, clinical, treatment, and laboratory data, including serial samples for viral RNA detection, were extracted from electronic medical records and compared between survivors and non-survivors. We used univariable and multivariable logistic regression methods to explore the risk factors associated with in-hospital death. Findings 191 patients (135 from Jinyintan Hospital and 56 from Wuhan Pulmonary Hospital) were included in this study, of whom 137 were discharged and 54 died in hospital. 91 (48%) patients had a comorbidity, with hypertension being the most common (58 [30%] patients), followed by diabetes (36 [19%] patients) and coronary heart disease (15 [8%] patients). Multivariable regression showed increasing odds of in-hospital death associated with older age (odds ratio 1·10, 95% CI 1·03–1·17, per year increase; p=0·0043), higher Sequential Organ Failure Assessment (SOFA) score (5·65, 2·61–12·23; p Interpretation The potential risk factors of older age, high SOFA score, and d-dimer greater than 1 μg/mL could help clinicians to identify patients with poor prognosis at an early stage. Prolonged viral shedding provides the rationale for a strategy of isolation of infected patients and optimal antiviral interventions in the future. Funding Chinese Academy of Medical Sciences Innovation Fund for Medical Sciences; National Science Grant for Distinguished Young Scholars; National Key Research and Development Program of China; The Beijing Science and Technology Project; and Major Projects of National Science and Technology on New Drug Creation and Development.

Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study

Complex networks arise in a wide range of biological and sociotechnical systems. Epidemic spreading is central to our understanding of dynamical processes in complex networks, and is of interest to physicists, mathematicians, epidemiologists, and computer and social scientists. This review presents the main results and paradigmatic models in infectious disease modeling and generalized social contagion processes.

Epidemic processes in complex networks

https://deim.urv.cat/~alexandre.arenas/publicacions/pdf/review.pdf

Synchronization in complex networks

By Matthew James Keelingand Pejman RohaniPrinceton, NJ: Princeton University Press,2008.408 pp., Illustrated. $65.00 (hardcover).Mathematical modeling of infectious dis-eases has progressed dramatically over thepast 3 decades and continues to ﬂourishat the nexus of mathematics, epidemiol-ogy, and infectious diseases research. Nowrecognized as a valuable tool, mathemat-ical models are being integrated into thepublic health decision-making processmore than ever before. However, despiterapid advancements in this area, a formaltraining program for mathematical mod-eling is lacking, and there are very fewbooks suitable for a broad readership. Tosupport this bridging science, a commonlanguage that is understood in all con-tributing disciplines is required.

Modeling Infectious Diseases in Humans and Animals

Seasonal variations in temperature, rainfall and resource availability are ubiquitous and can exert strong pressures on population dynamics. Infectious diseases provide some of the best-studied examples of the role of seasonality in shaping population fluctuations. In this paper, we review examples from human and wildlife disease systems to illustrate the challenges inherent in understanding the mechanisms and impacts of seasonal environmental drivers. Empirical evidence points to several biologically distinct mechanisms by which seasonality can impact host-pathogen interactions, including seasonal changes in host social behaviour and contact rates, variation in encounters with infective stages in the environment, annual pulses of host births and deaths and changes in host immune defences. Mathematical models and field observations show that the strength and mechanisms of seasonality can alter the spread and persistence of infectious diseases, and that population-level responses can range from simple annual cycles to more complex multiyear fluctuations. From an applied perspective, understanding the timing and causes of seasonality offers important insights into how parasite-host systems operate, how and when parasite control measures should be applied, and how disease risks will respond to anthropogenic climate change and altered patterns of seasonality. Finally, by focusing on well-studied examples of infectious diseases, we hope to highlight general insights that are relevant to other ecological interactions.

/pdf/seasonality-and-the-dynamics-of-infectious-diseases-1nbx7q5bgi.pdf

Seasonality and the dynamics of infectious diseases.

Dramatic changes in patterns of epidemics have been observed throughout this century. For childhood infectious diseases such as measles, the major transitions are between regular cycles and irregular, possibly chaotic epidemics, and from regionally synchronized oscillations to complex, spatially incoherent epidemics. A simple model can explain both kinds of transitions as the consequences of changes in birth and vaccination rates. Measles is a natural ecological system that exhibits different dynamical transitions at different times and places, yet all of these transitions can be predicted as bifurcations of a single nonlinear model.

https://science.sciencemag.org/content/sci/287/5453/667.full.pdf

A simple model for complex dynamical transitions in epidemics.

Background Mathematical models have become invaluable management tools for epidemiologists, both shedding light on the mechanisms underlying observed dynamics as well as making quantitative predictions on the effectiveness of different control measures. Here, we explain how substantial biases are introduced by two important, yet largely ignored, assumptions at the core of the vast majority of such models.
 
Methods and Findings First, we use analytical methods to show that (i) ignoring the latent period or (ii) making the common assumption of exponentially distributed latent and infectious periods (when including the latent period) always results in underestimating the basic reproductive ratio of an infection from outbreak data. We then proceed to illustrate these points by fitting epidemic models to data from an influenza outbreak. Finally, we document how such unrealistic a priori assumptions concerning model structure give rise to systematically overoptimistic predictions on the outcome of potential management options.
 
Conclusion This work aims to highlight that, when developing models for public health use, we need to pay careful attention to the intrinsic assumptions embedded within classical frameworks.

/pdf/appropriate-models-for-the-management-of-infectious-diseases-jhxa8kqx2y.pdf

Appropriate Models for the Management of Infectious Diseases

The management of infectious diseases is an increasingly important public health issue, the effective implementation of which is often complicated by difficulties in teasing apart the relative roles of extrinsic and intrinsic factors influencing transmission. Dengue, a vector-borne strain polymorphic disease, is one such infection where transmission dynamics are affected by environmental variables as well as immune-mediated serotype interactions. To understand how alternative hypotheses concerning dengue infection and transmission may explain observed multiannual cycles in disease incidence, we adopt a theoretical approach that combines both ecological and immunological mechanisms. We demonstrate that, contrary to perceived wisdom, patterns generated solely by antibody-dependent enhancement or heterogeneity in virus virulence are not consistent with serotype-specific notification data in important ways. Furthermore, to generate epidemics with the characteristic signatures observed in data, we find that a combination of seasonal variation in vector demography and, crucially, a short-lived period of cross-immunity is sufficient. We then show how understanding the persistence and eradication of dengue serotypes critically depends on the alternative assumed mechanisms.

/pdf/ecological-and-immunological-determinants-of-dengue-l4v30o4w6s.pdf

Pejman Rohani

Papers

Modeling Infectious Diseases in Humans and Animals

Seasonality and the dynamics of infectious diseases.

A simple model for complex dynamical transitions in epidemics.

Appropriate Models for the Management of Infectious Diseases

Ecological and immunological determinants of dengue epidemics