ON THE OPTIMAL VACCINATION STRATEGIES FOR HORIZONTALLY AND VERTICALLY TRANSMITTED INFECTIOUS DISEASES

We consider an SEIR epidemic model for an infectious disease that spreads in the human host population through both horizontal and vertical transmission. A periodically varying contact rate is introduced to simulate recurrent outbreaks. We use the optimal control theory to assess the disease control. Optimal vaccination strategies to minimize both the disease burden and the intervention costs are analyzed. We derive the optimality system and solve it numerically. The theoretical findings are then used to simulate a vaccination campaign for rubella under several scenarios, by using epidemiological parameters obtained by real data.

[1]  S. Sethi,et al.  Optimal Control of Some Simple Deterministic Epidemic Models , 1978 .

[2]  H. Hethcote,et al.  Simulations of rubella vaccination strategies in China. , 2006, Mathematical biosciences.

[3]  L Billings,et al.  Exciting chaos with noise: unexpected dynamics in epidemic outbreaks , 2002, Journal of mathematical biology.

[4]  H. Behncke.  Optimal control of deterministic epidemics , 2000 .

[5]  Alberto d'Onofrio,et al.  On pulse vaccination strategy in the SIR epidemic model with vertical transmission , 2005, Appl. Math. Lett..

[6]  Amit Huppert,et al.  Seasonal dynamics and thresholds governing recurrent epidemics , 2008, Journal of mathematical biology.

[7]  Suzanne Lenhart,et al.  Optimal control of treatments in a two-strain tuberculosis model , 2002 .

[8]  Holly Gaff,et al.  Optimal control applied to vaccination and treatment strategies for various epidemiological models. , 2009, Mathematical biosciences and engineering : MBE.

[9]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[10]  Michael Y. Li,et al.  Global Stability in Some Seir Epidemic Models , 2002 .

[11]  K. Wickwire.  Mathematical models for the control of pests and infectious diseases: a survey. , 1977, Theoretical population biology.

[12]  Herbert W. Hethcote,et al.  Optimal vaccination schedules in a deterministic epidemic model , 1973 .

[13]  Suzanne Lenhart,et al.  Backward Bifurcation and Optimal Control in Transmission Dynamics of West Nile Virus , 2010, Bulletin of mathematical biology.

[14]  Zhidong Teng,et al.  On a Nonautonomous SEIRS Model in Epidemiology , 2007, Bulletin of mathematical biology.

[15]  K. H. Wickwire,et al.  On the optimal control of a deterministic epidemic , 1974, Advances in Applied Probability.

[16]  Shingo Iwami,et al.  Optimal control strategy for prevention of avian influenza pandemic. , 2009, Journal of theoretical biology.

[17]  James S. Muldowney,et al.  A Geometric Approach to Global-Stability Problems , 1996 .

[18]  David Greenhalgh,et al.  THRESHOLD AND STABILITY RESULTS FOR AN SIRS EPIDEMIC MODEL WITH A GENERAL PERIODIC VACCINATION STRATEGY , 2005 .

[19]  Alberto d'Onofrio.  Globally stable vaccine-induced eradication of horizontally and vertically transmitted infectious diseases with periodic contact rates and disease-dependent demographic factors in the population , 2003, Appl. Math. Comput..

[20]  B. Buonomo,et al.  On the use of the geometric approach to global stability for three dimensional ODE systems: A bilinear case , 2008 .

[21]  I B Schwartz,et al.  Seasonality and period-doubling bifurcations in an epidemic model. , 1984, Journal of theoretical biology.

[22]  O. Diekmann.  Mathematical Epidemiology of Infectious Diseases , 1996 .

[23]  Xiao-Qiang Zhao,et al.  A Tuberculosis Model with Seasonality , 2010, Bulletin of mathematical biology.

[24]  Bruno Buonomo.  A simple analysis of vaccination strategies for rubella. , 2011, Mathematical biosciences and engineering : MBE.

[25]  L. Stone,et al.  Seasonal dynamics of recurrent epidemics , 2007, Nature.

[26]  Suzanne Lenhart,et al.  Optimal control of vaccine distribution in a rabies metapopulation model. , 2008, Mathematical biosciences and engineering : MBE.

[27]  Julien Arino,et al.  Global Results for an Epidemic Model with Vaccination that Exhibits Backward Bifurcation , 2003, SIAM J. Appl. Math..

[28]  I. A. Moneim,et al.  The effect of using different types of periodic contact rate on the behaviour of infectious diseases: A simulation study , 2007, Comput. Biol. Medicine.

[29]  V. Capasso.  Mathematical Structures of Epidemic Systems , 1993, Lecture Notes in Biomathematics.