Coupling the modeling of phage-bacteria interaction and cholera epidemiological model with and without optimal control.

Journal of Theoretical Biology
Hyacinthe M Ndongmo TeytsaJean Lubuma

Abstract

In this work, we assess the impact of the phage-bacteria infection and optimal control on the indirectly transmitted cholera disease. The phage-bacteria interactions are described by predator-prey system using the Smith functional response, which takes into account the number of bacteria binding sites. The study is done in two steps, namely the model without control and the model with control. For the first scenario, we explicitly compute the basic reproduction number R0 which serves as stability threshold and bifurcation parameter. The proposed model exhibits a bi-stability phenomenon via the existence of backward bifurcation, which implies that the classical requirement of bringing the reproduction number under unity, while necessary, is no longer sufficient for cholera elimination from the population. We intuitively introduce a new threshold number N0 needed for the global stability of the disease free equilibrium point which is achieved when R0⩽1 and N0⩽1. It is further shown that the phage absorption is a possible cause of bi-stability, since in its absence, the condition R0⩽1 is sufficient for cholera to die out. The existence of endemic equilibrium points depends on the range of both R0 and N0. Regarding the model extend...Continue Reading

References

Feb 24, 2001·BMC Infectious Diseases·C T Codeço
Oct 22, 2002·Mathematical Biosciences·P van den Driessche, James Watmough
Mar 5, 2003·Current Opinion in Microbiology·Brigid M Davis, Matthew K Waldor
Jun 25, 2008·Mathematical Biosciences·S M GarbaM R Abu Bakar
Sep 9, 2009·Mathematical Biosciences·Roberto C A ThoméLourdes Esteva
Jan 8, 2010·Bulletin of Mathematical Biology·Kbenesh W BlaynehTim Clayton
Oct 1, 2005·Mathematical Biosciences and Engineering : MBE·Julijana GjorgjievaCarlos Castillo-Chavez
Sep 1, 2004·Mathematical Biosciences and Engineering : MBE·Carlos Castillo-Chavez, Baojun Song
Jul 4, 2012·Lancet·Jason B HarrisStephen B Calderwood
Aug 14, 2012·Journal of Biological Dynamics·Majid Bani-YaghoubRenata Ivanek
Aug 19, 2014·Advances in Applied Microbiology·Samuel L Díaz-Muñoz, Britt Koskella
Aug 8, 2015·Computational and Mathematical Methods in Medicine·J B H Njagarah, F Nyabadza
Jun 21, 2016·Mathematical Biosciences·Hamadjam AbboubakarDaniel Tieudjo
Dec 23, 2016·Journal of Biological Dynamics·Xueying Wang, Jin Wang
Oct 7, 2017·BioEssays : News and Reviews in Molecular, Cellular and Developmental Biology·Ellie Harrison, Michael A Brockhurst
Jan 2, 2018·Mathematical Biosciences·Chayu Yang, Jin Wang
Feb 10, 2018·Mathematical Biosciences·Omprakash Singh SisodiyaJoydip Dhar

❮ Previous
Next ❯

Related Concepts

Related Feeds

Bacteriophage: Phage Therapy

Phage therapy uses bacterial viruses (bacteriophages) to treat bacterial infections and is widely being recognized as an alternative to antibiotics. Here is the latest research.