Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' threshold theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

On estimating the basic reproduction number in distinct stages of a contagious disease spreading

In epidemiology, the basic reproduction number R-0 is usually defined as the average number of new infections caused by a single infective individual introduced into a completely susceptible population. According to this definition. R-0 is related to the initial stage of the spreading of a contagious disease. However, from epidemiological models based on ordinary differential equations (ODE), R-0 is commonly derived from a linear stability analysis and interpreted as a bifurcation parameter: typically, when R-0 >1, the contagious disease tends to persist in the population because the endemic stationary solution is asymptotically stable: when R-0 <1, the corresponding pathogen tends to naturally disappear because the disease-free stationary solution is asymptotically stable. Here we intend to answer the following question: Do these two different approaches for calculating R-0 give the same numerical values? In other words, is the number of secondary infections caused by a unique sick individual equal to the threshold obtained from stability analysis of steady states of ODE? For finding the answer, we use a susceptibleinfective-recovered (SIR) model described in terms of ODE and also in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. The values of R-0 obtained from both approaches are compared, showing good agreement. (C) 2012 Elsevier B.V. All rights reserved.

Reproduction in Gammarus (Crustacea, Amphipoda): basic processes

Research on the basic reproduction processes of Gammarus is summarized and reviewed, reproductive strategies in males and females being left to two later papers. The author describes the reproductive systems, the development of eggs (oocytes) in the ovaries, courtship and precopulatory amplexus, mating and the production of sperms, egg laying, mortality and diapause.

A simple model for the establishment of tick-borne pathogens of Ixodes scapularis : a global sensitivity analysis of R0

The basic reproduction number of a pathogen, R 0, determines whether a pathogen will spread (R0>1R 0>1), when introduced into a fully susceptible population or fade out (R0<1R 0<1), because infected hosts do not, on average, replace themselves. In this paper we develop a simple mechanistic model for the basic reproduction number for a group of tick-borne pathogens that wholly, or almost wholly, depend on horizontal transmission to and from vertebrate hosts. This group includes the causative agent of Lyme disease, Borrelia burgdorferi, and the causative agent of human babesiosis, Babesia microti, for which transmission between co-feeding ticks and vertical transmission from adult female ticks are both negligible. The model has only 19 parameters, all of which have a clear biological interpretation and can be estimated from laboratory or field data. The model takes into account the transmission efficiency from the vertebrate host as a function of the days since infection, in part because of the potential for this dynamic to interact with tick phenology, which is also included in the model. This sets the model apart from previous, similar models for R0 for tick-borne pathogens. We then define parameter ranges for the 19 parameters using estimates from the literature, as well as laboratory and field data, and perform a global sensitivity analysis of the model. This enables us to rank the importance of the parameters in terms of their contribution to the observed variation in R0. We conclude that the transmission efficiency from the vertebrate host to Ixodes scapularis ticks, the survival rate of Ixodes scapularis from fed larva to feeding nymph, and the fraction of nymphs finding a competent host, are the most influential factors for R0. This contrasts with other vector borne pathogens where it is usually the abundance of the vector or host, or the vector-to-host ratio, that determine conditions for emergence. These results are a step towards a better understanding of the geographical expansion of currently emerging horizontally transmitted tick-borne pathogens such as Babesia microti, as well as providing a firmer scientific basis for targeted use of acaricide or the application of wildlife vaccines that are currently in development.

A Generalist Predator Regulating Spread of a Wildlife Disease: Exploring Two Infection Transmission Scenarios

Ecoepidemiology is a well-developed branch of theoretical ecology, which explores interplay between the trophic interactions and the disease spread. In most ecoepidemiological models, however, the authors assume the predator to be a specialist, which consumes only a single prey species. In few existing papers, in which the predator was suggested to be a generalist, the alternative food supply was always considered to be constant. This is obviously a simplification of reality, since predators can often choose between a number of different prey. Consumption of these alternative prey can dramatically change their densities and strongly influence the model predictions. In this paper, we try to bridge the gap and explore a generic ecoepidemiological system with a generalist predator, where the densities of all prey are dynamical variables. The model consists of two prey species, one of which is subject to an infectious disease, and a predator, which consumes both prey species. We investigate two main scenarios of infection transmission mode: (i) the disease transmission rate is predator independent and (ii) the transmission rate is a function of predator density. For both scenarios we fulfil an extensive bifurcation analysis. We show that including a second dynamical prey in the system can drastically change the dynamics of the single prey case. In particular, the presence of a second prey impedes disease spread by decreasing the basic reproduction number and can result in a substantial drop of the disease prevalence. We demonstrate that with efficient consumption of the second prey species by the predator, the predator-dependent disease transmission can not destabilize interactions, as in the case with a specialist predator. Interestingly, even if the population of the second prey eventually vanishes and only one prey species finally remains, the system with two prey species may exhibit different properties to those of the single prey system.

A mathematical model for the dynamics of Banana Xanthomonas Wilt with vertical transmission and inflorescence infection

A mathematical model for Banana Xanthomonas Wilt (BXW) spread by insect is presented. The model incorporates inflorescence infection and vertical transmission from the mother corm to attached suckers, but not tool-based transmission by humans. Expressions for the basic reproduction number R0 are obtained and it is verified that disease persists, at a unique endemic level, when R0 > 1. From sensitivity analysis, inflorescence infection rate and roguing rate were the parameters with most influence on disease persistence and equilibrium level. Vertical transmission parameters had less effect on persistence threshold values. Parameters were approximately estimated from field data. The model indicates that single stem removal is a feasible approach to eradication if spread is mainly via inflorescence infection. This requires continuous surveillance and debudding such that a 50% reduction in inflorescence infection and 2–3 weeks interval of surveillance would eventually lead to full recovery of banana plantations and hence improved production.

Epidemiologia delle strongilosi dell'asino: quali applicazioni per il controllo delle infezioni da elminti?

Strongylosis in equids, despite being very common, have never been studied from a strictly ecological point of view. Mathematical models are important ecological tools used to study the temporal dynamics of parasite populations, and are useful to study the effect of different biological parameters, as well as to analyse the outcome produced by perturbations such as anthelmintic treatments. This work describes the study of the temporal dynamics of strongyles infection in an organic donkey population, performed using coprological quantitative analysis and donkeys’ age as a proxy of the time of infection. Force of infection was then estimated for Strongylus vulgaris and small strongyles and the results used as the basis for the development of mathematical models. In particular, the comparison of models output and field data made it possible to estimate the transmission coefficient  and to consequently calculate the basic reproduction number R0 and the threshold host density. Small strongyles model includes hypobiosis and, more interestingly as never found in literature, a density-dependent development rate of hypobiotic larvae in adult parasites in order to simulate a negative feedback between larvae emergence from hypobiosis and adult parasite abundance. Simulations of pharmacological and environmental treatments showed that parasite eradication was possible for S. vulgaris only, while small strongyles, due to hypobiosis and density-dependent development rate of their hypobiotic larvae, are very difficult to control and impossible to eradicate. In addition, density-dependence in larval development has been demonstrated to act as a key factor in improving parasite population survival and abundance even in absence of human intervention.

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.

Rapid drop in the reproduction number during the Ebola outbreak in the Democratic Republic of Congo.

The Democratic Republic of Congo (DRC) experienced a confined rural outbreak of Ebola virus disease (EVD) with 69 reported cases from July to October 2014. Understanding the transmission dynamics during the outbreak can provide important information for anticipating and controlling future EVD epidemics. I fitted an EVD transmission model to previously published data of this outbreak and estimated the basic reproduction number R 0 = 5.2 (95% CI [4.0-6.7]). The model suggests that the net reproduction number Rt fell below unity 28 days (95% CI [25-34] days) after the onset of symptoms in the index case. This study adds to previous epidemiological descriptions of the 2014 EVD outbreak in DRC, and is consistent with the notion that a rapid implementation of control interventions helped reduce further spread.

The Metapopulation Dynamics of an Infectious Disease: Tuberculosis in Possums

An SEI metapopulation model is developed for the spread of an infectious agent by migration. The model portrays two age classes on a number of patches connected by migration routes which are used as host animals mature. A feature of this model is that the basic reproduction ratio may be computed directly, using a scheme that separates topography, demography, and epidemiology. We also provide formulas for individual patch basic reproduction numbers and discuss their connection with the basic reproduction ratio for the system. The model is applied to the problem of spatial spread of bovine tuberculosis in a possum population. The temporal dynamics of infection are investigated for some generic networks of migration links, and the basic reproduction ratio is computed—its value is not greatly different from that for a homogeneous model. Three scenarios are considered for the control of bovine tuberculosis in possums where the spatial aspect is shown to be crucial for the design of disease management operations

Adaptability of Damara, Dorper and Traditional Meat Sheep Breeds in Semi-Arid Queensland

Reproductive rate is a major contributing factor to the profitability of a sheep meat enterprise. Low reproduction rate is a feature of sheep husbandry in semi-arid Queensland. High ambient temperatures are implicated in poor fertility (Moule 1970) where variation in response can be due to breed and to animals within a breed (Hopkins and Stephenson 1978). Breeds recently imported from South Africa were selected in arid environments and may be better adapted to pastoral conditions of northern Australia than traditional breeds. Animal production for a consuming world : proceedings of 9th Congress of the Asian-Australasian Association of Animal Production Societies [AAAP] and 23rd Biennial Conference of the Australian Society of Animal Production [ASAP] and 17th Annual Symposium of the University of Sydney, Dairy Research Foundation, [DRF]. 2-7 July 2000, Sydney, Australia. This study will investigate (a) the thermoregulatory ability of Damara, Dorper, Poll Dorset, Rambouillet, South African Meat Merino and Queensland medium wool Merino rams prior to joinings in the autumn and spring of 1999, 2000 and 2001 and (b) the association between thermoregulatory parameters (rectal temperature and respiration rate) and ewe fertility. Results for the initial autumn joining are reported in this paper.

Control dynamics of severe acute respiratory syndrome transmission

Severe acute respiratory syndrome (SARS) is a serious disease with many puzzling features. We present a simple, dynamic model to assess the epidemic potential of SARS and the effectiveness of control measures. With this model, we analysed the SARS epidemic data in Beijing. The data fitting gives the basic case reproduction number of 2.16 leading to the outbreak, and the variation of the effective reproduction number reflecting the control effect. Noticeably, our study shows that the response time and the strength of control measures have significant effects on the scale of the outbreak and the lasting time of the epidemic.

Flowering in British Lemna: A rare, cyclic or simply overlooked phenomenon?

It is largely presumed that reproduction in British Lemna, as in other British Lemnaceae, is almost entirely asexual, with new daughter fronds being produced from the side pouches of older mother fronds. Sexual reproduction is considered to be a rather rare event or even absent and because of this rarity the sexual features of Lemna, such as anthers and fruit, are often considered to be of little taxonomic value. It was with some surprise, therefore, that widespread flowering was observed in all British Lemna during the summer of 1995. Initial observations in Shropshire during June recorded flowers in minor and trisulca, with fruit production in trisulca. L.gibba, minor and minuta were noted as being in flower on several occasions in Kent, during July and August, probably fruit production occurring in both species. To what extent these events are truly representative of the sexual reproduction rate of British Lemna on a year-to-year basis, or simply reflect the unusually high summer temperatures of 1995, is unclear.

Laboratory culture of Moina with organic ana inorganic fertilizers

An experiment was conducted in the laboratory condition to determine the effect of organic (poultry drop, cow dung and mustard oil cake) and inorganic fertilizer (urea) on production, reproduction rate and maturation time of Moina species. Production rate was also determined in both aerated and non-aerated system in plastic containers with carrying capacity of 2.5-liter each. Total production was significantly higher in both aerated (2475 individuals/2.5 l water) and non-aerated (3253 individuals/2.5 l water) containers using poultry manure compared to other fertilizers. Moreover, the reproduction rate and maturation time in poultry drops showed distinct efficacy in Moina species. Reproduction rate of 11 individuals was the maximal while lowest maturation time was found 78 hours. Reproduction and maturation were induced surprisingly in test tube where the aeration system was absent.

Effect of two green algae species (Chlorella sp. & Scenedesmus obliquus) enriched with B group vitamins on food chain of Rutilus frisii kutum (Kamensky, 1901) fry

The Effect of two freshwater green algae species Chlorella sp. & Scenedesmus obliquus enriched (from the beginning of culture and after 96 hours) with different dosages of B group vitamins (0, 0.5, 1, and 2 ml of enriching solution per each liter of algae medium) on fecundity of Daphnia magna and growth of Rutilus frisii kutum fry were investigated in a research from spring, 2008 to autumn, 2009. First, each of the green algae species were cultured purely and massively in the Zander (Z-8+N) medium and then the nutritional value (the amount of protein, lipid, and carbohydrate) of enriched algae were meausered. In this study, enriching of Chlorella sp. & S. obliquus with a suitable mix of B group vitamins significantly improved their nutritive value. So the highest amount of nutritional value of Chlorella sp. was obtained because of enriching with dosage 0.5 ml.l-1 (366.654Kcal) and for Scenedesmus obliquus with dosage of 1 ml.l-1 (376.95Kcal). The acquired amount from control group showed an increase of respectively 42% and 11%. According to the results, increased dosages of enriching solution caused Daphnia fecundity to increase (at both stages : enrichment from the beginning of culture and after 96 hours). So the highest average of D. magna reproduction rate was obtained through being fed with Chlorella sp. and S. obliquus enriched with dosage of 2 ml enriching solution per liter of algae medium. The average fecundity of D. magna fed with Chlorella sp. enriched with dosage of 2 ml.l-1 enriching solution from the beginning of culture and after 96 hours was obtained respectively 2.128 ± 0.375 and 2.1 ± 0.69 and the average fecundity of D. magna fed with S. obliquus enriched with dosage of 2 ml enriching solution from the beginning of culture and after 96 hours was obtained respectively 2.128 ± 0.375 and 2.1 ± 0.69 which showed respectively an increase of 61 ٪, 91٪, 77 ٪, and 83٪ in proportion to the acquired amount from control group. When enriching solution was added to either algae culture medium from the beginning of culture, showed statistically significant differences (P<0.05) between dosages of 0 and 2 ml.l-1, 1 and 2 ml.l-1, and 0.5 and 2 ml enriching solution per each liter of Chlorella sp. culture medium and between dosages of 0 and 1 ml.l-1, and 0 and 2 ml enriching solution per each liter of S. obliquus culture medium. The highest average of body weight gain percentage and specific growth rate of kutum fry was obtained respectively 21.19%, 26.63%, 1.92, and 2.34 from the beginning of culture and after 96 hours with dosage of 1 ml B group vitamins per each liter of Chlorella sp. culture medium, which showed respectively an increase of 50%, 70%, 46%, and 62% in proportion to the acquired amount from control group. In the cases which Chlorella sp. were grown in the medium containing vitamin, from point of view of the average percentage of weight and specific growth rate of kutum fry significant differences were observed on the basis of the result of One-way ANOVA between dosages of 0 and 1, 1 and 2 , 0.5 and 1 ml B group vitamins per each liter. The highest average of body weight gain percentage and specific growth rate of kutum fry was obtained respectively 32.02%, 29.42%, 2.78, and 2.34 from the beginning of culture and after 96 hours with dosage of 2 ml B group vitamins per each liter of S. obliquus culture medium, which showed respectively an increase of 32%, 19%, 28%, and 17% in proportion to the acquired amount from control group. In the cases which S. obliquus were grown in the medium containing vitamin, from point of view of the average percentage of weight and specific growth rate of kutum fry significant differences were observed on the basis of the result of One-way ANOVA between dosages of 0 and 1, 0 and 2. According to the results of the present research we can say that considerable enhancement in the quality of the food of D. magna can be made by manipulation of the nutritional value of fresh water unicellular green algae with suitable mixture of B group vitamins, so that both the fecundity of D. magna will increase and the nutritional requirements of the kutum fry will be filled in this way.