scholarly journals Variation of constants formula and exponential dichotomy for nonautonomous non-densely defined Cauchy problems

2020 ◽  
pp. 1-43
Author(s):  
Pierre Magal ◽  
Ousmane Seydi
Keyword(s):  
Exponential Dichotomy ◽  
Homogeneous Problem ◽  
Cauchy Problems ◽  
Small Perturbations ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Age Structured ◽  
Necessary And Sufficient ◽  
Age Structured Model ◽  
Densely Defined

Abstract In this paper, we extend to the non-Hille–Yosida case a variation of constants formula for a nonautonomous and nonhomogeneous Cauchy problems first obtained by Gühring and Räbiger. By using this variation of constants formula, we derive a necessary and sufficient condition for the existence of an exponential dichotomy for the evolution family generated by the associated nonautonomous homogeneous problem. We also prove a persistence result of the exponential dichotomy for small perturbations. Finally, we illustrate our results by considering two examples. The first example is a parabolic equation with nonlocal and nonautonomous boundary conditions, and the second example is an age-structured model that is a hyperbolic equation.

Travelling wave solutions for an infection-age structured model with diffusion

2009 ◽  
Vol 139 (3) ◽  
pp. 459-482 ◽  
Author(s):  
A. Ducrot ◽  
P. Magal
Keyword(s):  
Travelling Waves ◽  
Travelling Wave ◽  
Sufficient Condition ◽  
Travelling Wave Solutions ◽  
Necessary And Sufficient Condition ◽  
Infection Age ◽  
Age Of Infection ◽  
Age Structured ◽  
Necessary And Sufficient ◽  
Age Structured Model

In this article, we study the existence of travelling waves for a class of epidemic models structured in space and with respect to the age of infection. We obtain a necessary and sufficient condition for the existence of travelling waves for such a class of problems. As a consequence of our main result, we also derive the existence of travelling waves of a class of functional partial derivative equations.

scholarly journals The emergence of rabbit haemorrhagic disease virus: will a non-pathogenic strain protect the UK?

2001 ◽  
Vol 356 (1411) ◽  
pp. 1087-1095 ◽  
Author(s):  
P.J. White ◽  
R.A. Norman ◽  
R.C. Trout ◽  
E.A. Gould ◽  
P.J. Hudson
Keyword(s):  
Disease Virus ◽  
Pathogenic Strain ◽  
Rabbit Haemorrhagic Disease Virus ◽  
Rabbit Haemorrhagic Disease ◽  
Seroprevalence Data ◽  
Age Structured ◽  
Reproductive Rates ◽  
The Uk ◽  
Haemorrhagic Disease ◽  
Age Structured Model

Rabbit haemorrhagic disease virus emerged in China in 1984, and has killed hundreds of millions of wild rabbits in Australia and Europe. In the UK there appears to be an endemic non–pathogenic strain, with high levels of seroprevalence being recorded, in the absence of associated mortality. Using a seasonal, age–structured model we examine the hypothesis that differences in rabbit population demography differentially affect the basic reproductive rates ( R 0 ) of the pathogenic and non–pathogenic strains, leading to each dominating in some populations and not others. The strain with the higher R 0 excluded the other, with the dynamics depending upon the ratio of the two R 0 values. When the non–pathogenic strain dominated, the pathogenic strain caused only transient mortality, although this could be significant when the two R 0 values were similar. When the pathogenic strain dominated, repeated epidemics led to host eradication. Seroprevalence data suggest that the non–pathogenic strain may be protecting some, but not all UK populations, with half being ‘at risk’ from invasion by the pathogenic strain and a fifth prone to significant transient mortality. We identify key questions for empirical research to test this prediction.

POTENTIAL YIELD OF A ROCK SHRIMP STOCK, SICYONIA PENICILLATA IN THE NORTHERN GULF OF CALIFORNIA

Crustaceana ◽  
1999 ◽  
Vol 72 (6) ◽  
pp. 581-590 ◽  
Author(s):  
Juana Lopez-Martinez ◽  
Edgar Alcantara-Razo ◽  
Sergio Hernandez-Vazquez ◽  
Ernesto Chavez
Keyword(s):  
Gulf Of California ◽  
Age Groups ◽  
Potential Yield ◽  
Natural Oscillations ◽  
Recruitment Pattern ◽  
Stock Recruitment ◽  
Age Structured ◽  
Stochastic Recruitment ◽  
Age Structured Model ◽  
Compensatory Effect

AbstractA stock of rock shrimp Sicyonia penicillata was assessed in a fishery recently opened at Bahoa Kino, Sonora, Mexico. An age-structured model with stochastic recruitment was developed, which considers growth rate, natural mortality, and fishing mortality by age. Age groups were followed year by year with a stock-recruitment Ricker function where the seasonal recruitment pattern was defined as well. Simulations might be interpreted as showing a stable population with four year cycles, reflecting a density-dependent process. In 1996, fishing intensity had an apparent compensatory effect on the stock, decreasing the amplitude of natural oscillations and maintaining the stock at a biomass level similar to the size observed in a condition of no exploitation. The stock was found currently underexploited. As a result of the seasonal accessibility and the age of first-catch fishing (adult shrimp), the stock might be capable to withstand high fishing pressure without being overexploited. Se evaluo una poblacion de camaron de roca Sicyonia penicillata, de una pesqueroa recientemente abierta en Bahoa Kino, Sonora, Mexico. Se desarrollo un modelo basado en la estructura por edades que considera reclutamiento estocastico, tasa de crecimiento, mortalidad natural y mortalidad por pesca por grupo de edad. Estos grupos de edad fueron determinados ano tras ano mediante la funcion de reclutamiento de Ricker, en los que tambien se definio el patron estacional de reclutamiento. Las simulaciones muestran una poblacion estable con ciclos de cuatro anos, que indican un proceso de densodependencia. En 1996, la intensidad de pesca tuvo un efecto compensatorio sobre la poblacion, reduciendo la amplitud de las oscilaciones naturales y manteniendo al stock en un nivel de biomasa similar al observado en la condicion sin explotacion. Se encontro que el recurso esta subexplotado. Como resultado de la accesibilidad estacional y de que la edad de primera captura corresponde a camaron adulto, el recurso soporta alta presion de pesca sin dar evidencias de sobreexplotacion.

scholarly journals The development and validation of an age-structured model for the evaluation of disease control strategies for intestinal helminths

Parasitology ◽  
1994 ◽  
Vol 109 (3) ◽  
pp. 389-396 ◽  
Author(s):  
M. S. Chan ◽  
H. L. Guyatt ◽  
D. A. P. Bundy ◽  
G. F. Medley
Keyword(s):  
Helminth Infection ◽  
Control Strategies ◽  
Intestinal Helminth ◽  
Intestinal Helminths ◽  
Parasite Control ◽  
Age Related ◽  
Control Programmes ◽  
Age Structured ◽  
Development And Validation ◽  
Age Structured Model

SummaryEpidemiological modelling can be a useful tool for the evaluation of parasite control strategies. An age-structured epidemiological model of intestinal helminth dynamics is developed. This model includes the explicit representation of changing worm distributions between hosts as a result of treatment, and estimates the morbidity due to heavy infections. The model is used to evaluate the effectiveness of different programmes of age-targeted community chemotherapy in reducing the amount of morbidity due to helminth infection. The magnitude of age-related heterogeneities is found to be very important in determining the results of age-targeted treatment programmes. The model was verified using field data from control programmes for Ascaris lumbricoides and Trichuris trichiura, and was found to provide accurate predictions of prevalence and mean intensities of infection during and following different control regimes.

Sign in / Sign up

Export Citation Format

Share Document