Dengue disease, basic reproduction number and control

Dengue is one of the major international public health concerns. Although progress is underway, developing a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control. A model for the transmission of Dengue disease is presented. It consists of eight mutually exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquito. The model presents three possible equilibria: two disease-free equilibria (DFE) and another endemic equilibrium. It has been proved that a DFE is locally asymptotically stable, whenever a certain epidemiological threshold, known as the basic reproduction number, is less than one. We show that if we apply a minimum level of insecticide, it is possible to maintain the basic reproduction number below unity. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.Comment: This is a preprint of a paper whose final and definitive form has appeared in International Journal of Computer Mathematics (2011), DOI: 10.1080/00207160.2011.55454

The basic reproduction number, R0R_0, in structured populations

In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, $R_0$, for Markovian epidemics in structured populations. The methodology derived is applicable to, and demonstrated on, both $SIR$ and $SIS$ epidemics and allows for population as well as epidemic dynamics. The approach taken is to consider the epidemic process as a multitype process by identifying and classifying the different types of infectious units along with the infections from, and the transitions between, infectious units. For the household model, we show that our expression for $R_0$ agrees with earlier work despite the alternative nature of the construction of the mean reproductive matrix, and hence, the basic reproduction number.Comment: 26 page

The net reproduction rate and the type-reproduction number in multiregional demography

In order to study effects of migration on demographic changes of multiregional populations, multiregional population modelling is a useful traditional tool. Although multiregional mathematical demography has been extensively explored since the beginning of the 1970s, its key concept, the multiregional net reproduction rate, has been long neglected. In this review, we focus on a multiregional stable population system and elaborate the definition of the multiregional net reproduction rate. Next we introduce the type-reproduction number from mathematical epidemiology and show that it becomes a useful index to formulate a simple control relation for a multiregional population. Mathematical ideas presented here will help us to reconsider multiregional mathematical demography, which is a useful theoretical framework to study effects of interregional migration on population dynamics and composition.

Global dynamics of a periodic SEIRS model with general incidence rate

We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate and it is shown the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence. Numerical simulations are per- formed to estimate the basic reproduction number and illustrate our analytical findings, using a nonlinear incidence rate

Estimating the reproduction number of Ebola virus (EBOV) during the 2014 outbreak in West Africa

The 2014 Ebola virus (EBOV) outbreak in West Africa is the largest outbreak of the genus Ebolavirus to date. To better understand the spread of infection in the affected countries, it is crucial to know the number of secondary cases generated by an infected index case in the absence and presence of control measures, i.e., the basic and effective reproduction number. In this study, I describe the EBOV epidemic using an SEIR (susceptible-exposed-infectious-recovered) model and fit the model to the most recent reported data of infected cases and deaths in Guinea, Sierra Leone and Liberia. The maximum likelihood estimates of the basic reproduction number are 1.51 (95% confidence interval [CI]: 1.50-1.52) for Guinea, 2.53 (95% CI: 2.41-2.67) for Sierra Leone and 1.59 (95% CI: 1.57-1.60) for Liberia. The model indicates that in Guinea and Sierra Leone the effective reproduction number might have dropped to around unity by the end of May and July 2014, respectively. In Liberia, however, the model estimates no decline in the effective reproduction number by end-August 2014. This suggests that control efforts in Liberia need to be improved substantially in order to stop the current outbreak.Comment: Published version, PLOS Currents Outbreaks. 2014 Sep

Systematic evaluation of the population-level effects of alternative treatment strategies on the basic reproduction number

An approach to estimate the influence of the treatment-type controls on the basic reproduction number, R 0 , is proposed and elaborated. The presented approach allows one to estimate the effect of a given treatment strategy or to compare a number of different treatment strategies on the basic reproduction number. All our results are valid for sufficiently small values of the control. However, in many cases it is possible to extend this analysis to larger values of the control as was illustrated by examples

Differences between the true reproduction number and the apparent reproduction number of an epidemic time series

The time-varying reproduction number $R(t)$ measures the number of new infections per infectious individual and is closely correlated with the time series of infection incidence by definition. The timings of actual infections are rarely known, and analysis of epidemics usually relies on time series data for other outcomes such as symptom onset. A common implicit assumption, when estimating $R(t)$ from an epidemic time series, is that $R(t)$ has the same relationship with these downstream outcomes as it does with the time series of incidence. However, this assumption is unlikely to be valid given that most epidemic time series are not perfect proxies of incidence. Rather they represent convolutions of incidence with uncertain delay distributions. Here we define the apparent time-varying reproduction number, $R_A(t)$, the reproduction number calculated from a downstream epidemic time series and demonstrate how differences between $R_A(t)$ and $R(t)$ depend on the convolution function. The mean of the convolution function sets a time offset between the two signals, whilst the variance of the convolution function introduces a relative distortion between them. We present the convolution functions of epidemic time series that were available during the SARS-CoV-2 pandemic. Infection prevalence, measured by random sampling studies, presents fewer biases than other epidemic time series. Here we show that additionally the mean and variance of its convolution function were similar to that obtained from traditional surveillance based on mass-testing and could be reduced using more frequent testing, or by using stricter thresholds for positivity. Infection prevalence studies continue to be a versatile tool for tracking the temporal trends of $R(t)$, and with additional refinements to their study protocol, will be of even greater utility during any future epidemics or pandemics

Substituting for families? Schools and social reproduction in AIDS-affected Lesotho

This is the post-print version of the final published article that is available from the link below. Copyright @ 2008 Editorial Board of Antipode.Families, the state and employers all have a broad if differentiated interest in securing the daily and generational reproduction of society. Whereas in Western countries, the past two decades have witnessed a progressive displacement of responsibility for social reproduction from the state to families, in southern Africa, day-to-day social reproduction has always remained overwhelmingly the preserve of families. Today, however, the AIDS pandemic is radically transforming family life for many children, and prompting concerns (arguably a moral panic) about the potential breakdown of social reproduction. Even in Africa, schools have long supplemented families in delivering generational reproduction, albeit geared around the transfer of “factual” knowledge and with a narrow focus on preparing new generations of workers. In light of the AIDS pandemic, a number of commentators have suggested ways in which schools could further substitute for the diminishing capacities of families. Based on interviews with decision-makers and analysis of policy documents, I explore a number of interventions being enacted in Lesotho's schools. I argue that such initiatives remain small in scale and often justified in relation to retaining children in school. In practice both government and employers remain more interested in the generational reproduction of workers than in daily reproduction. If the welfare needs of AIDS-affected children are to be met through schooling, there is a need for the education sector's role to be understood in relation to an ethics of care, rather than the functionalist production of a future workforce.RGS-IBG Small Research Gran

Lunar cycles of reproduction in the clown anemonefish Amphiprion percula: individual-level strategies and population-level patterns

Lunar cycles of reproduction are a widespread phenomenon in marine invertebrates and vertebrates. It is common practice to infer the adaptive value of this behavior based on the population level pattern. This practice may be flawed if individuals within the population are employing different reproductive strategies. Here, we capitalize on a long-term field study and a carefully controlled laboratory experiment of individually identifiable clown anemonefish, Amphiprion percula, to investigate the individual reproductive strategies underlying population-level patterns of reproduction. The field data reveal that A. percula exhibit a lunar cycle of reproduction at the population level. Further, the field data reveal that there is naturally occurring variation among individuals and within individuals in the number of times they reproduce per month. The laboratory experiment reveals that the number of times individuals reproduce per month is dependent on their food availability. Individuals are employing a conditional strategy, breeding once, twice or thrice per month, depending on resource availability. Breaking down the population level pattern by reproductive tactic, we show that each reproductive tactic has its own non-random lunar cycle of reproduction. Considering the adaptive value of these cycles, we suggest that all individuals, regardless of tactic, may avoid reproducing around the new moon. Further, individuals may avoid breeding in synchrony with each other, because of negative frequency dependent selection at the time of settlement. Most importantly, we conclude that determining what individuals are doing is a critical step toward understanding the adaptive value of lunar cycles of reproduction