Approximation of the Basic Reproduction Number R 0 for Vector-Borne Diseases with a Periodic Vector Population

Institut de Recherche pour le Développement (IRD), 32 avenue Henri Varagnat, 93143 Bondy Cedex, France.
Bulletin of Mathematical Biology (Impact Factor: 1.39). 04/2007; 69(3):1067-91. DOI: 10.1007/s11538-006-9166-9
Source: PubMed


The main purpose of this paper is to give an approximate formula involving two terms for the basic reproduction number R(0) of a vector-borne disease when the vector population has small seasonal fluctuations of the form p(t) = p(0) (1+epsilon cos(omegat - phi)) with epsilon < 1. The first term is similar to the case of a constant vector population p but with p replaced by the average vector population p(0). The maximum correction due to the second term is (epsilon(2)/8)% and always tends to decrease R(0). The basic reproduction number R(0) is defined through the spectral radius of a linear integral operator. Four numerical methods for the computation of R(0) are compared using as example a model for the 2005/2006 chikungunya epidemic in La Réunion. The approximate formula and the numerical methods can be used for many other epidemic models with seasonality.

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    • "The European-wide projections for A. albopictus account for changing patterns of activity phase or/and climatic suitability [12,262728. Frequently, spatial risk analyses for CHIKV transmission are based on calculating (and mapping) the basic reproduction number R 0 [30,474849. However, in the case of CHIKV in Europe this type of modelling can be very misleading as one key factor for such models is the vector density, which is not yet known [50] . "
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    ABSTRACT: (Please note: As this is a conference contribution, there is currently no full-text version available. The final results will be published in a separate paper.) Background: Following its introduction in Europe, Aedes albopictus has spread throughout many areas of the Mediterranean basin. In 2007, the mosquito mediated an outbreak of Chikungunya, with nearly 200 people infected. The extent to which climate changes will alter the distribution range of Aedes albopictus and possibilities for Chikungunya transmission in Europe remain important questions for public health. Methods: Ecological niche modelling was conducted to assess the climatic suitability for Aedes albopictus and Chikungunya. The impact of climate change on the climatic suitability for Chikungunya transmission was then modelled based on the A1B and B1 climate scenarios for 2011-2040, 2041-2070 and 2071-2100 (modelling work is in progress to develop projections under IPCC RCP 4.5 and RCP6 climate scenarios). Regions at risk were compared with regions deemed to have the lowest adaptive capacities in Europe, based upon a previous ECDC study. Results: Climate change will likely lead to shifts in the climatically suitable areas for Aedes albopictus and for Chikungunya virus transmission in Europe. Relatively speaking, climate change impacts are projected to increase in central Western Europe, such as France, Belgium and Luxembourg, and Germany. The currently suitable Mediterranean regions are projected to remain this way, with the exception of the southernmost areas of Europe which could become too dry. When considering adaptive capacities alongside projected impacts, some areas within the Pannonian Basin in East-Central Europe (comprising parts of Hungary, Croatia, Slovakia, Serbia, Slovenia and Romania), had the highest overall risk profile due to an increase in projected impacts and lower anticipated adaptive capacities. Conclusions: Understanding preparedness priorities for vector-borne disease necessitates assessments of how climate changes may affect suitable climates for disease transmission, as well as consideration of a broad range of other factors such as disease introduction risks and the adaptive capacities and underlying health status of populations at-risk. This assessment may be used to assist preparedness planners by providing information about where measures such as enhanced vector-surveillance, information-raising, and vector control activities could prove helpful.
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    • "In order to reflect the effect of demographic behavior of individuals, scholars have recognized that age-structured epidemic models are more realistic, since any disease prevention policy depends on the age structure of host population, and instantaneous death and infection rates depend on the age. Since the pioneer work of McKendrick [3], many authors have studied various age-structured epidemic models [2, 7–12]. "
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    ABSTRACT: We formulate an age-structured SIS epidemic model with periodic parameters, which includes host population and vector population. The host population is described by two partial differential equations, and the vector population is described by a single ordinary differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on locally integrable periodic functions. We obtain that if the spectral radius of the Fréchet derivative of the fixed point operator at zero is greater than one, there exists a unique endemic periodic solution, and we investigate the global attractiveness of disease-free steady state of the normalized system.
    Full-text · Article · Feb 2015 · Journal of Applied Mathematics
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    • "In what follows, we use the definition of Bacaër and Guernaoui [4] (see also Bacaër [5]) and the general calculation method in Wang and Zhao [36] to evaluate the basic reproduction number R 0 for system (3.1). Then we analyze the threshold dynamics of system (3.1). "
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