The basic reproduction number (R0), also called the basic reproduction ratio or rate or the basic reproductive rate, is an epidemiologic metric used to describe the contagiousness or transmissibility of infectious agents. R0 is affected by numerous biological, sociobehavioral, and environmental factors that govern pathogen transmission and, therefore, is usually estimated with various types of complex mathematical models, which make R0 easily misrepresented, misinterpreted, and misapplied. R0 is not a biological constant for a pathogen, a rate over time, or a measure of disease severity, and R0 cannot be modified through vaccination campaigns. R0 is rarely measured directly, and modeled R0 values are dependent on model structures and assumptions. Some R0 values reported in the scientific literature are likely obsolete. R0 must be estimated, reported, and applied with great caution because this basic metric is far from simple.

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Complexity of the Basic Reproduction Number (R0).

The potential impact of an influenza pandemic can be assessed by calculating a set of transmissibility parameters, the most important being the reproduction number (R), which is defined as the average number of secondary cases generated per typical infectious case We conducted a systematic review to summarize published estimates of R for pandemic or seasonal influenza and for novel influenza viruses (eg H5N1) We retained and summarized papers that estimated R for pandemic or seasonal influenza or for human infections with novel influenza viruses The search yielded 567 papers Ninety-one papers were retained, and an additional twenty papers were identified from the references of the retained papers Twenty-four studies reported 51 R values for the 1918 pandemic The median R value for 1918 was 180 (interquartile range [IQR]: 147–227) Six studies reported seven 1957 pandemic R values The median R value for 1957 was 165 (IQR: 153–170) Four studies reported seven 1968 pandemic R values The median R value for 1968 was 180 (IQR: 156–185) Fifty-seven studies reported 78 2009 pandemic R values The median R value for 2009 was 146 (IQR: 130–170) and was similar across the two waves of illness: 146 for the first wave and 148 for the second wave Twenty-four studies reported 47 seasonal epidemic R values The median R value for seasonal influenza was 128 (IQR: 119–137) Four studies reported six novel influenza R values Four out of six R values were <1 These R values represent the difference between epidemics that are controllable and cause moderate illness and those causing a significant number of illnesses and requiring intensive mitigation strategies to control Continued monitoring of R during seasonal and novel influenza outbreaks is needed to document its variation before the next pandemic

https://link.springer.com/content/pdf/10.1186%2F1471-2334-14-480.pdf

Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature

Background: In developing countries, most people with mental, neurological and substance-abuse (MNS) disorders do not receive adequate care mainly because of a lack of mental health professionals. Non-specialist health workers, but also other professionals with health roles, such as teachers, may therefore have an important role to play in delivering MNS health care. Researchers in The Cochrane Collaboration carried out a review of the effects of using non-specialist health workers or other professionals with health roles to help people with MNS disorders in developing countries. After searching for all relevant studies in scientific databases, they found 38 studies published before October 2012. Their findings are summarised below. What is a non-specialist health worker? Any type of health worker (like a doctor, nurse or lay health worker) who is not a specialist in mental health or neurology but who may have had some training in these fields. We also looked at teachers, as they can be particularly important in the care of children and youths. What the research says: The studies in this review were from 22 developing countries. In most studies, lay health workers delivered the mental health care, and addressed depression or anxiety (or both), or post-traumatic stress disorder. The review shows that the use of non-specialist health workers, compared with usual healthcare services: Â· may increase the number of adults who recover from depression or anxiety (or both) two to six months after treatment; Â· may slightly reduce symptoms formothers with depression; Â· may slightly reduce the symptoms of adults with post-traumatic stress disorder (non-specialists and teachers were used in one study); Â· probably slightly improves the symptoms of people with dementia; Â· probably improves/slightly improves the mental well-being, burden and distress of carers of people with dementia; Â· may decrease the quantity of alcohol consumed by problem drinkers. It is uncertain whether lay health workers or teachers reducepost-traumatic stress disorder symptoms among children. There were too few studies to draw any conclusions about the cost-effectiveness of using non-specialist health workers or teachers, or about their impact on people with other MNS conditions such as epilepsy, schizophrenia, and alcohol and drug abuse problems. In addition, very few studies measured unintended consequences of non-specialist health worker-led care - such effects could impact on the appropriateness and quality of care. Quality of the evidence: Overall, non-specialist health workers and teachers have some promising benefits in improving people's outcomes for general and perinatal depression, post-traumatic stress disorder and alcohol-use disorders, and patient and carer outcomes for dementia. However, this evidence is of low or very low quality in some areas, and for some issues no evidence is available. Therefore, we cannot make conclusions about which specific interventions using non-specialist health workers to help people with MNS disorders are more effective.

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Non-specialist health worker interventions for the care of mental, neurological and substance-abuse disorders in low- and middle-income countries.

Objective: To characterize patient and programmatic factors associated with retention in care during the pre-antiretroviral therapy (ART) period and linkage to ART care. Design: Systematic literature review. Methods: An electronic search was conducted on MEDLINE, Global Health, Google Scholar and conference databases to identify studies reporting on predictors, barriers and facilitators of retention in care in the pre-ART period, and linkage to care at three steps: ART-eligibility assessment, pre-ART care and ART initiation. Factors associated with attrition were then divided into areas for intervention. Results: Seven hundred and sixty-eight citations were identified. Forty-twostudies from 12 countries were included for review, with the majority from South Africa (16). The most commonly cited category of factors was transport costs and distance. Stigma and fear of disclosure comprised the second most commonly cited category of factors followed by staff shortages, long waiting times, fear of drug side effects, male sex, younger age and the need to take time off work. Conclusion: This review highlights the importance of investigating interventions that could reduce transport difficulties. Decentralization, task-shifting and integration of services need to be expedited to alleviate health system barriers. Patient support groups and strategic posttest counselling are essential to assist patients deal with stigma and disclosure. Moreover, well tolerated first-line drugs and treatment literacy programmes are needed to improve acceptance of ART. This review suggests a combination of interventions to retain specific groups at risk for attrition such as workplace programmes for employed patients, dedicated clinic and support programmes for men and younger individuals. 2012 Wolters Kluwer Health | Lippincott Williams & Wilkins AIDS 2012, 26:2059‐2067

Risk factors, barriers and facilitators for linkage to antiretroviral therapy care: a systematic review.

Recent epidemics of Zika, dengue, and chikungunya have heightened the need to understand the seasonal and geographic range of transmission by Aedes aegypti and Ae. albopictus mosquitoes. We use mechanistic transmission models to derive predictions for how the probability and magnitude of transmission for Zika, chikungunya, and dengue change with mean temperature, and we show that these predictions are well matched by human case data. Across all three viruses, models and human case data both show that transmission occurs between 18-34°C with maximal transmission occurring in a range from 26-29°C. Controlling for population size and two socioeconomic factors, temperature-dependent transmission based on our mechanistic model is an important predictor of human transmission occurrence and incidence. Risk maps indicate that tropical and subtropical regions are suitable for extended seasonal or year-round transmission, but transmission in temperate areas is limited to at most three months per year even if vectors are present. Such brief transmission windows limit the likelihood of major epidemics following disease introduction in temperate zones.

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Detecting the impact of temperature on transmission of Zika, dengue, and chikungunya using mechanistic models.

The basic reproductive ratio, 𝑅0, is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if 𝑅0l1, the disease dies out, whereas if 𝑅0g1, the disease persists. 𝑅0 has been widely used as a measure of disease strength to estimate the effectiveness of control measures and to form the backbone of disease-management policy. However, in almost every aspect that matters, 𝑅0 is flawed. Diseases can persist with 𝑅0l1, while diseases with 𝑅0g1 can die out. We show that the same model of malaria gives many different values of 𝑅0, depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values of 𝑅0 for a variety of diseases, and examine some of the alternatives that have been proposed. If 𝑅0 is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.

The failure of R0.

The Failure of R 0

There has been a sudden increase in the amount of money donors are willing to spend on the worldwide HIV/AIDS epidemic. Present plans are to hold most of the money in reserve and spend it slowly. However, rapid spending may be the best strategy for halting this disease. We develop a mathematical model that predicts eradication or persistence of HIV/AIDS on a world scale. Dividing the world into regions (continents, countries etc), we develop a linear differential equation model of infectives which has the same eradication properties as more complex models. We show that, even if HIV/AIDS can be eradicated in each region independently, travel/immigration of infectives could still sustain the epidemic. We use a continent-level example to demonstrate that eradication is possible if preventive intervention methods (such as condoms or education) reduced the infection rate to two fifths of what it is currently. We show that, for HIV/AIDS to be eradicated within five years, the total cost would be ≈ $63 billion, which is within the existing $60 billion (plus interest) amount raised by the donor community. However, if this action is spread over a twenty year period, as currently planned, then eradication is no longer possible, due to population growth, and the costs would exceed $90 billion. Eradication of AIDS is feasible, using the tools that we have currently to hand, but action needs to occur immediately. If not, then HIV/AIDS will race beyond our ability to afford it.

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Can we spend our way out of the AIDS epidemic? A world halting AIDS model

Modeling Spatial Spread of Infectious Diseases with a Fixed Latent Period in a Spatially Continuous Domain

In this paper, with the assumptions that an infectious disease in a popula- tion has a fixed latent period and the latent individuals of the population may disperse, we formulate an SIR model with a simple demographic structure for the popula- tion living in ann-patch environment (cities, towns, or countries, etc.). The model is given by a system of delay differential equations with a fixed delay accounting for the latencyandanon-localtermcausedbythemobilityoftheindividualsduringthelatent period. Assuming irreducibility of the travel matrices of the infection related classes, an expression for the basic reproduction number R0 is derived, and it is shown that the disease free equilibrium is globally asymptotically stable if R0 1. In the latter case, there is at least one endemic equilibrium and the disease will be uniformly persistent. When n = 2, two special cases allowing reduc- ible travel matrices are considered to illustrate joint impact of the disease latency and population mobility on the disease dynamics. In addition to the existence of the dis- ease free equilibrium and interior endemic equilibrium, the existence of a boundary equilibrium and its stability are discussed for these two special cases.

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Jing Li

Papers

The failure of R0.

The Failure of R 0

Can we spend our way out of the AIDS epidemic? A world halting AIDS model

Modeling Spatial Spread of Infectious Diseases with a Fixed Latent Period in a Spatially Continuous Domain

Dynamics of an epidemic model with non-local infections for diseases with latency over a patchy environment.