G.J. Boender

Mapping the basic reproduction number (R0) for vector-borne diseases: A case study on bluetongue virus

Geographical maps indicating the value of the basic reproduction number, R₀, can be used to identify areas of higher risk for an outbreak after an introduction. We develop a methodology to create R₀ maps for vector-borne diseases, using bluetongue virus as a case study. This method provides a tool for gauging the extent of environmental effects on disease emergence. The method involves integrating vector-abundance data with statistical approaches to predict abundance from satellite imagery and with the biologically mechanistic modelling that underlies R₀. We illustrate the method with three applications for bluetongue virus in the Netherlands: 1) a simple R₀ map for the situation in September 2006, 2) species-specific R₀ maps based on satellite-data derived predictions, and 3) monthly R₀ maps throughout the year. These applications ought to be considered as a proof-of-principle and illustrations of the methods described, rather than as ready-to-use risk maps. Altogether, this is a first step towards an integrative method to predict risk of establishment of diseases based on mathematical modelling combined with a geographic information system that may comprise climatic variables, landscape features, land use, and other relevant factors determining the risk of establishment for bluetongue as well as of other emerging vector-borne diseases.

The transmission potential of Rift Valley fever virus among livestock in the Netherlands: a modelling study

AbstractsRift Valley fever virus (RVFV) is a zoonotic vector-borne infection and causes a potentially severe disease. Many mammals are susceptible to infection including important livestock species. Although currently confined to Africa and the near-East, this disease causes concern in countries in temperate climates where both hosts and potential vectors are present, such as the Netherlands. Currently, an assessment of the probability of an outbreak occurring in this country is missing. To evaluate the transmission potential of RVFV, a mathematical model was developed and used to determine the initial growth and the Floquet ratio, which are indicators of the probability of an outbreak and of persistence in a periodic changing environment caused by seasonality. We show that several areas of the Netherlands have a high transmission potential and risk of persistence of the infection. Counter-intuitively, these are the sparsely populated livestock areas, due to the high vector-host ratios in these areas. Culex pipiens s.l. is found to be the main driver of the spread and persistence, because it is by far the most abundant mosquito. Our investigation underscores the importance to determine the vector competence of this mosquito species for RVFV and its host preference.

Risk based surveillance for early detection of low pathogenic avian influenza outbreaks in layer chickens

Current knowledge does not allow the prediction of when low pathogenic avian influenza virus (LPAIV) of the H5 and H7 subtypes infecting poultry will mutate to their highly pathogenic phenotype (HPAIV). This mutation may already take place in the first infected flock; hence early detection of LPAIV outbreaks will reduce the likelihood of pathogenicity mutations and large epidemics. The objective of this study was the development of a model for the design and evaluation of serological-surveillance programmes, with a particular focus on early detection of LPAIV infections in layer chicken flocks. Early detection is defined as the detection of an infected flock before it infects on average more than one other flock (between-flock reproduction ratio Rf<1), hence a LPAI introduction will be detected when only one or a few other flocks are infected. We used a mathematical model that investigates the required sample size and sampling frequency for early detection by taking into account the LPAIV within- and between-flock infection dynamics as well as the diagnostic performance of the serological test used. Since layer flocks are the target of the surveillance, we also explored whether the use of eggs, is a good alternative to sera, as sample commodity. The model was used to refine the current Dutch serological-surveillance programme. LPAIV transmission-risk maps were constructed and used to target a risk-based surveillance strategy. In conclusion, we present a model that can be used to explore different sampling strategies, which combined with a cost-benefit analysis would enhance surveillance programmes for low pathogenic avian influenza.

Derivation of a Floquet Formalism within a Natural Framework

Many biological systems experience a periodic environment. Floquet theory is a mathematical tool to deal with such time periodic systems. It is not often applied in biology, because linkage between the mathematics and the biology is not available. To create this linkage, we derive the Floquet theory for natural systems. We construct a framework, where the rotation of the Earth is causing the periodicity. Within this framework the angular momentum operator is introduced to describe the Earth’s rotation. The Fourier operators and the Fourier states are defined to link the rotation to the biological system. Using these operators, the biological system can be transformed into a rotating frame in which the environment becomes static. In this rotating frame the Floquet solution can be derived. Two examples demonstrate how to apply this natural framework.