Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Severe acute respiratory syndrome coronavirus 2 is the causative agent of the ongoing coronavirus disease pandemic. Initial estimates of the early dynamics of the outbreak in Wuhan, China, suggested a doubling time of the number of infected persons of 6-7 days and a basic reproductive number (R0) of 2.2-2.7. We collected extensive individual case reports across China and estimated key epidemiologic parameters, including the incubation period (4.2 days). We then designed 2 mathematical modeling approaches to infer the outbreak dynamics in Wuhan by using high-resolution domestic travel and infection data. Results show that the doubling time early in the epidemic in Wuhan was 2.3-3.3 days. Assuming a serial interval of 6-9 days, we calculated a median R0 value of 5.7 (95% CI 3.8-8.9). We further show that active surveillance, contact tracing, quarantine, and early strong social distancing efforts are needed to stop transmission of the virus.

https://stacks.cdc.gov/view/cdc/90194/cdc_90194_DS1.pdf

High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2

Mathematical models of transmission have become invaluable management tools in planning for the control of emerging infectious diseases. A key variable in such models is the reproductive number R. For new emerging infectious diseases, the value of the reproductive number can only be inferred indirectly from the observed exponential epidemic growth rate r. Such inference is ambiguous as several different equations exist that relate the reproductive number to the growth rate, and it is unclear which of these equations might apply to a new infection. Here, we show that these different equations differ only with respect to their assumed shape of the generation interval distribution. Therefore, the shape of the generation interval distribution determines which equation is appropriate for inferring the reproductive number from the observed growth rate. We show that by assuming all generation intervals to be equal to the mean, we obtain an upper bound to the range of possible values that the reproductive number may attain for a given growth rate. Furthermore, we show that by taking the generation interval distribution equal to the observed distribution, it is possible to obtain an empirical estimate of the reproductive number.

/pdf/how-generation-intervals-shape-the-relationship-between-3fkay9cy62.pdf

How generation intervals shape the relationship between growth rates and reproductive numbers.

The United Nations Children's Fund, or UNICEF, was originally created to provide relief for children in countries devastated by the destruction of World War II. After 1950, UNICEF turned to focus on general programs for the improvement of children's welfare worldwide, and in 1965, it was awarded the Nobel Prize for Peace for its humanitarian efforts. The organization concentrates on areas in which relatively small expenditures can have a significant impact on the lives of the most disadvantaged children in developing countries, such as the prevention and treatment of disease, child healthcare, malnutrition, illiteracy, and other welfare services.

The United Nations Children's Fund

Dengue is a spectrum of disease caused by four serotypes of the most prevalent arthropod-borne virus affecting humans today, and its incidence has increased dramatically in the past 50 years. Due in part to population growth and uncontrolled urbanization in tropical and subtropical countries, breeding sites for the mosquitoes that transmit dengue virus have proliferated, and successful vector control has proven problematic. Dengue viruses have evolved rapidly as they have spread worldwide, and genotypes associated with increased virulence have expanded from South and Southeast Asia into the Pacific and the Americas. This review explores the human, mosquito, and viral factors that contribute to the global spread and persistence of dengue, as well as the interaction between the three spheres, in the context of ecological and climate changes. What is known, as well as gaps in knowledge, is emphasized in light of future prospects for control and prevention of this pandemic disease.

/pdf/global-spread-and-persistence-of-dengue-4jert0rib2.pdf

Global spread and persistence of dengue.

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

Ecological and immunological determinants of dengue epidemics

Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus

Case notifications of pertussis have shown an increase in a number of countries with high rates of routine pediatric immunization. This has led to significant public health concerns over a possible pertussis re-emergence. A leading proposed explanation for the observed increase in incidence is the loss of immunity to pertussis, which is known to occur after both natural infection and vaccination. Little is known, however, about the typical duration of immunity and its epidemiological implications. Here, we analyze a simple mathematical model, exploring specifically the inter-epidemic period and fade-out frequency. These predictions are then contrasted with detailed incidence data for England and Wales. We find model output to be most sensitive to assumptions concerning naturally acquired immunity, which allows us to estimate the average duration of immunity. Our results support a period of natural immunity that is, on average, long-lasting (at least 30 years) but inherently variable.

/pdf/estimating-the-duration-of-pertussis-immunity-using-4hkxa3gfcp.pdf

Estimating the duration of pertussis immunity using epidemiological signatures.

Author(s): Stoddard, Steven T; Wearing, Helen J; Reiner, Robert C; Morrison, Amy C; Astete, Helvio; Vilcarromero, Stalin; Alvarez, Carlos; Ramal-Asayag, Cesar; Sihuincha, Moises; Rocha, Claudio; Halsey, Eric S; Scott, Thomas W; Kochel, Tadeusz J; Forshey, Brett M | Abstract: IntroductionLong-term disease surveillance data provide a basis for studying drivers of pathogen transmission dynamics. Dengue is a mosquito-borne disease caused by four distinct, but related, viruses (DENV-1-4) that potentially affect over half the world's population. Dengue incidence varies seasonally and on longer time scales, presumably driven by the interaction of climate and host susceptibility. Precise understanding of dengue dynamics is constrained, however, by the relative paucity of laboratory-confirmed longitudinal data.MethodsWe studied 10 years (2000-2010) of laboratory-confirmed, clinic-based surveillance data collected in Iquitos, Peru. We characterized inter and intra-annual patterns of dengue dynamics on a weekly time scale using wavelet analysis. We explored the relationships of case counts to climatic variables with cross-correlation maps on annual and trimester bases.FindingsTransmission was dominated by single serotypes, first DENV-3 (2001-2007) then DENV-4 (2008-2010). After 2003, incidence fluctuated inter-annually with outbreaks usually occurring between October and April. We detected a strong positive autocorrelation in case counts at a lag of ∼ 70 weeks, indicating a shift in the timing of peak incidence year-to-year. All climatic variables showed modest seasonality and correlated weakly with the number of reported dengue cases across a range of time lags. Cases were reduced after citywide insecticide fumigation if conducted early in the transmission season.ConclusionsDengue case counts peaked seasonally despite limited intra-annual variation in climate conditions. Contrary to expectations for this mosquito-borne disease, no climatic variable considered exhibited a strong relationship with transmission. Vector control operations did, however, appear to have a significant impact on transmission some years. Our results indicate that a complicated interplay of factors underlie DENV transmission in contexts such as Iquitos.

https://escholarship.org/content/qt14m2f4dj/qt14m2f4dj.pdf?t=qajkkh

Helen J. Wearing

Papers

Appropriate Models for the Management of Infectious Diseases

Ecological and immunological determinants of dengue epidemics

Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus

Estimating the duration of pertussis immunity using epidemiological signatures.

Long-Term and Seasonal Dynamics of Dengue in Iquitos, Peru