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rotavirusR2 - Journal of Mathematical Biology manuscript...

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Journal of Mathematical Biology manuscript No. (will be inserted by the editor) E. Shim · Z. Feng · M. Martcheva · C. Castillo-Chavez An age-structured epidemic model of rotavirus with vaccination Received: date / Revised: date Abstract The recent approval of a rotavirus vaccine in Mexico motivates this study on the potential impact of the use of such a vaccine on rotavirus prevention and control. An age-structured model that describes the rotavirus transmission dynamics of infections is introduced. Conditions that guarantee the local and global stability analysis of the disease-free steady state distri- bution as well as the existence of an endemic steady state distribution are established. The impact of maternal antibodies on the implementation of vac- cine is evaluated. Model results are used to identify optimal age-dependent vaccination strategies. A convergent numerical scheme for the model is intro- duced but not implemented. This paper is dedicated to Prof. K. P. Hadeler, who continues to push the frontier of knowledge in mathematical biology. Keywords rotavirus · age-structure · vacccination Mathematics Subject Classification (2000) 92D30 · 65N06 · 65N12 E. Shim and C. Castillo-Chavez Department of Mathematics and Statistics Arizona State University P.O. Box 871804, Tempe, AZ 85287-1804 Tel.: 480-727-9004 Fax: 480-727-7346 E-mail: [email protected] Z. Feng Department of Mathematics Purdue University 150 N. University Street, West Lafayette, IN 47907-2067 M. Martcheva Department of Mathematics University of Florida P.O.Box 118105, Gainesville, FL 32611-8105
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2 E. Shim et al. 1 Introduction The discovery of rotavirus ([4]) as the major etiologic agent of diarrhea in infants and young children has had a dramatic impact on public health policy programs geared towards the reductions of diarrhea morbidity and mortality over the last three decades. 95% of children worldwide have experienced a rotavirus infection with most infections in the 3 to 5 year age-range [24]. The highest rate of infection occurs in infants between 6 and 24 months of age [18]. Mortality from rotavirus diarrhea is quite low but morbidity is still high. In the United States rotavirus infections affect approximately 2.7 million children under 5 years of age and result in the hospitalization of 55 , 000 children every year [24]. The direct costs on U.S. medical care have been estimated to be around $274 million [24]. The overall cost associated with rotavirus infections has been estimated at more than $1 billion per year, in the United States alone [24]. Over 600 , 000 children die annually worldwide [7]. The primary mode of rotavirus transmission is fecal-oral [15]. Reported low titers of virus in respiratory tract secretions and other body fluids repre- sent (less common) secondary transmission routes. Rotavirus can survive for months at room temperature and it is resistant to chloroform, ether, fluoro- carbons, CsCl, non-ionic detergents and pH 4-9 [27]. Rotavirus can be passed from one person to another through a set of contaminated hands with the virus or by touching a contaminated surface or object. The virus enters the body through the mouth. Children can spread rotavirus before and after they
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