
Previous Article
A natural differential operator on conic spaces
 PROC Home
 This Issue

Next Article
A longtime stable fully discrete approximation of the CahnHilliard equation with inertial term
A mathematical model for the spread of streptococcus pneumoniae with transmission due to sequence type
1.  Department of Statistics and Modelling Science, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH 
2.  Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26, Richmond Street, Gasgow G1 1XH, United Kingdom, United Kingdom 
We start off with a discussion of Streptococcus pneumoniae and a review of previous work. We propose a simple mathematical model with two sequence types and then perform an equilibrium and (global) stability analysis on the model. We show that in general there are only three equilibria, the carriagefree equilibrium and two carriage equilibria. If the effective reproduction number $R_e$ is less than or equal to one, then the carriage will die out. If $R_e$ > 1, then the carriage will tend to the carriage equilibrium corresponding to the multilocus sequence type with the largest transmission parameter. In the case where both multilocus sequence types have the same transmission parameter then there is a line of carriage equilibria. Provided that carriage is initially present then as time progresses the carriage will approach a point on this line. The results generalize to many competing sequence types. Simulations with realistic parameter values confirm the analytical results.
[1] 
Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete and Continuous Dynamical Systems  B, 2013, 18 (1) : 3756. doi: 10.3934/dcdsb.2013.18.37 
[2] 
Marc Briant. Stability of global equilibrium for the multispecies Boltzmann equation in $L^\infty$ settings. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 66696688. doi: 10.3934/dcds.2016090 
[3] 
Franco Maceri, Michele Marino, Giuseppe Vairo. Equilibrium and stability of tensegrity structures: A convex analysis approach. Discrete and Continuous Dynamical Systems  S, 2013, 6 (2) : 461478. doi: 10.3934/dcdss.2013.6.461 
[4] 
Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595607. doi: 10.3934/mbe.2007.4.595 
[5] 
Nitu Kumari, Sumit Kumar, Sandeep Sharma, Fateh Singh, Rana Parshad. Basic reproduction number estimation and forecasting of COVID19: A case study of India, Brazil and Peru. Communications on Pure and Applied Analysis, , () : . doi: 10.3934/cpaa.2021170 
[6] 
Rolf Rannacher. A short course on numerical simulation of viscous flow: Discretization, optimization and stability analysis. Discrete and Continuous Dynamical Systems  S, 2012, 5 (6) : 11471194. doi: 10.3934/dcdss.2012.5.1147 
[7] 
Gerardo Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, J. M. Hyman. The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 14551474. doi: 10.3934/mbe.2013.10.1455 
[8] 
Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. Stability analysis of inhomogeneous equilibrium for axially and transversely excited nonlinear beam. Communications on Pure and Applied Analysis, 2011, 10 (5) : 14471462. doi: 10.3934/cpaa.2011.10.1447 
[9] 
C. Burgos, J.C. Cortés, L. Shaikhet, R.J. Villanueva. A delayed nonlinear stochastic model for cocaine consumption: Stability analysis and simulation using real data. Discrete and Continuous Dynamical Systems  S, 2021, 14 (4) : 12331244. doi: 10.3934/dcdss.2020356 
[10] 
Toshikazu Kuniya, Yoshiaki Muroya. Global stability of a multigroup SIS epidemic model for population migration. Discrete and Continuous Dynamical Systems  B, 2014, 19 (4) : 11051118. doi: 10.3934/dcdsb.2014.19.1105 
[11] 
Matthew Macauley, Henning S. Mortveit. Update sequence stability in graph dynamical systems. Discrete and Continuous Dynamical Systems  S, 2011, 4 (6) : 15331541. doi: 10.3934/dcdss.2011.4.1533 
[12] 
Andrea Bondesan, Laurent Boudin, Marc Briant, Bérénice Grec. Stability of the spectral gap for the Boltzmann multispecies operator linearized around nonequilibrium maxwell distributions. Communications on Pure and Applied Analysis, 2020, 19 (5) : 25492573. doi: 10.3934/cpaa.2020112 
[13] 
Yirmeyahu J. Kaminski. Equilibrium locus of the flow on circular networks of cells. Discrete and Continuous Dynamical Systems  S, 2018, 11 (6) : 11691177. doi: 10.3934/dcdss.2018066 
[14] 
Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure and Applied Analysis, 2006, 5 (3) : 515528. doi: 10.3934/cpaa.2006.5.515 
[15] 
Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure and Applied Analysis, 2007, 6 (1) : 6982. doi: 10.3934/cpaa.2007.6.69 
[16] 
Ken Shirakawa. Stability analysis for phase field systems associated with crystallinetype energies. Discrete and Continuous Dynamical Systems  S, 2011, 4 (2) : 483504. doi: 10.3934/dcdss.2011.4.483 
[17] 
Zhiqi Lu. Global stability for a chemostattype model with delayed nutrient recycling. Discrete and Continuous Dynamical Systems  B, 2004, 4 (3) : 663670. doi: 10.3934/dcdsb.2004.4.663 
[18] 
Napoleon Bame, Samuel Bowong, Josepha Mbang, Gauthier Sallet, JeanJules Tewa. Global stability analysis for SEIS models with n latent classes. Mathematical Biosciences & Engineering, 2008, 5 (1) : 2033. doi: 10.3934/mbe.2008.5.20 
[19] 
Weiyi Zhang, Ling Zhou. Global asymptotic stability of constant equilibrium in a nonlocal diffusion competition model with free boundaries. Discrete and Continuous Dynamical Systems  B, 2022, 27 (12) : 77457782. doi: 10.3934/dcdsb.2022062 
[20] 
Tianhui Yang, Lei Zhang. Remarks on basic reproduction ratios for periodic abstract functional differential equations. Discrete and Continuous Dynamical Systems  B, 2019, 24 (12) : 67716782. doi: 10.3934/dcdsb.2019166 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]