Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures

Computational and Mathematical Methods in Medicine
Joshua Kiddy K AsamoahHemen Dutta

Abstract

Vaccination and treatment are the most effective ways of controlling the transmission of most infectious diseases. While vaccination helps susceptible individuals to build either a long-term immunity or short-term immunity, treatment reduces the number of disease-induced deaths and the number of infectious individuals in a community/nation. In this paper, a nonlinear deterministic model with time-dependent controls has been proposed to describe the dynamics of bacterial meningitis in a population. The model is shown to exhibit a unique globally asymptotically stable disease-free equilibrium ℰ0, when the effective reproduction number ℛVT ≤ 1, and a globally asymptotically stable endemic equilibrium ℰ1, when ℛVT > 1; and it exhibits a transcritical bifurcation at ℛVT = 1. Carriers have been shown (by Tornado plot) to have a higher chance of spreading the infection than those with clinical symptoms who will sometimes be bound to bed during the acute phase of the infection. In order to find the best strategy for minimizing the number of carriers and ill individuals and the cost of control implementation, an optimal control problem is set up by defining a Lagrangian function L to be minimized subject to the proposed model. Numerical...Continue Reading

References

Jun 5, 2003·Emerging Infectious Diseases·Stephen B GordonSteve M Graham
May 8, 2007·Emerging Infectious Diseases·Garry B CoulsonUNKNOWN Group for Enteric, Respiratory and Meningeal Disease Surveillance in South Africa
Jun 8, 2007·Emerging Infectious Diseases·Judith E MuellerPierre Nicolas
Jun 30, 2007·Mathematical Biosciences·Seema NandaSuzanne Lenhart
Jul 12, 2007·International Journal of Health Geographics·Hélène BroutinJean-François Guégan
Jun 24, 2008·Journal of Theoretical Biology·Simeone MarinoDenise E Kirschner
Jul 1, 2008·Bio Systems·Gul ZamanIl Hyo Jung
Jul 2, 2009·Mathematical Biosciences and Engineering : MBE·Holly Gaff, Elsa Schaefer
May 27, 2011·The New England Journal of Medicine·Michael C ThigpenUNKNOWN Emerging Infections Programs Network
Jul 26, 2011·Epidemiology and Infection·T J IrvingC L Trotter
Jan 1, 2013·Vaccine·UNKNOWN Dakar discussion group on priorities for research on epidemic meningococcal disease in AfricaGuy Vernet
Jan 9, 2013·Transactions of the Royal Society of Tropical Medicine and Hygiene·Lydiane AgierStéphane Hugonnet
Feb 13, 2013·Computer Methods and Programs in Biomedicine·Daniela Iacoviello, Nicolino Stasio
May 9, 2013·Journal of Mathematical Biology·Ahmed AbdelrazecHuaiping Zhu
Jul 11, 2013·Drugs·Amanda C Cohn, Lee H Harrison
May 6, 2014·Computational and Mathematical Methods in Medicine·Saul C MpesheYaw Nkansah-Gyekye
Aug 7, 2014·Computational and Mathematical Methods in Medicine·Baba Seidu, Oluwole D Makinde
Nov 11, 2015·Clinical Infectious Diseases : an Official Publication of the Infectious Diseases Society of America·Andromachi KarachaliouCaroline L Trotter

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Citations

Oct 31, 2019·Computational and Mathematical Methods in Medicine·Getachew Teshome Tilahun

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