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# Approximation of the basic reproduction number R0 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: 1.29). 04/2007; 69(3):1067-91. DOI: 10.1007/s11538-006-9166-9 Source: PubMed

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**ABSTRACT:**Seasonal fluctuations have been observed in many infectious diseases. Discrete epidemic models with periodic epidemiological parameters are formulated and studied to take into account seasonal variations of infectious diseases. The definition and the formula of the basic reproduction number R 0 are given by following the framework in [1,2,3,4,5]. Threshold results for a general model are obtained which show that the magnitude of R 0 determines whether the disease will go extinct (when R 0 <1) or not (when R 0 >1) in the population. Applications of these general results to discrete periodic SIR and SEIS models are demonstrated. The disease persistence and the existence of the positive periodic solution are established. Numerical explorations of the model properties are also presented via several examples including the calculations of the basic reproduction number, conditions for the disease extinction or persistence, and the existence of periodic solutions as well as its stability.Discrete and Continuous Dynamical Systems - Series B 01/2013; 1(1). · 0.63 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper investigates a RVF epidemic model by qualitative analysis and numerical simulations. Qualitative analysis have been used to explore the stability dynamics of the equilibrium points while visualization techniques such as bifurcation diagrams, Poincaré maps, maxima return maps and largest Lyapunov exponents are numerically computed to confirm further complexity of these dynamics induced by the seasonal forcing on the mosquitoes oviposition rates. The obtained results show that ordinary differential equation models with external forcing can have rich dynamic behaviour, ranging from bifurcation to strange attractors which may explain the observed fluctuations found in RVF empiric outbreak data, as well as the non deterministic nature of RVF inter-epidemic activities. Furthermore, the coexistence of the endemic equilibrium is subjected to existence of certain number of infected Aedes mosquitoes, suggesting that Aedes have potential to initiate RVF epidemics through transovarial transmission and to sustain low levels of the disease during post epidemic periods. Therefore we argue that locations that may serve as RVF virus reservoirs should be eliminated or kept under control to prevent multi-periodic outbreaks and consequent chains of infections. The epidemiological significance of this study is: (1) low levels of birth rate (in both Aedes and Culex) can trigger unpredictable outbreaks; (2) Aedes mosquitoes are more likely capable of inducing unpredictable behaviour compared to the Culex; (3) higher oviposition rates on mosquitoes do not in general imply manifestation of irregular behaviour on the dynamics of the disease. Finally, our model with external seasonal forcing on vector oviposition rates is able to mimic the linear increase in livestock seroprevalence during inter-epidemic period showing a constant exposure and presence of active transmission foci. This suggests that RVF outbreaks partly build upon RVF inter-epidemic activities. Therefore, active RVF surveillance in livestock is recommended.PLoS ONE 10/2014; 9(10):e108172. · 3.53 Impact Factor -
##### Article: Chikungunya Viral Fitness Measures within the Vector and Subsequent Transmission Potential.

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**ABSTRACT:**Given the recent emergence of chikungunya in the Americas, the accuracy of forecasting and prediction of chikungunya transmission potential in the U.S. requires urgent assessment. The La Reunion-associated sub-lineage of chikungunya (with a valine substitution in the envelope protein) was shown to increase viral fitness in the secondary vector, Ae. albopictus. Subsequently, a majority of experimental and modeling efforts focused on this combination of a sub-lineage of the East-Central-South African genotype (ECSA-V) - Ae. albopictus, despite the Asian genotype being the etiologic agent of recent chikungunya outbreaks world-wide. We explore a collection of data to investigate relative transmission efficiencies of the three major genotypes/sub-lineages of chikungunya and found difference in the extrinsic incubation periods to be largely overstated. However, there is strong evidence supporting the role of Ae. albopictus in the expansion of chikungunya that our R0 calculations cannot attribute to fitness increases in one vector over another. This suggests other ecological factors associated with the Ae. albopictus-ECSA-V cycle may drive transmission intensity differences. With the apparent bias in literature, however, we are less prepared to evaluate transmission where Ae. aegypti plays a significant role. Holistic investigations of CHIKV transmission cycle(s) will allow for more complete assessment of transmission risk in areas affected by either or both competent vectors.PLoS ONE 10/2014; 9(10):e110538. · 3.53 Impact Factor

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