Analysis of an age-structured dengue model with multiple strains and cross immunity
- 1 January 2021
- journal article
- research article
- Published by University of Szeged in Electronic Journal of Qualitative Theory of Differential Equations
- No. 50,p. 1-30
- https://doi.org/10.14232/ejqtde.2021.1.50
Abstract
Dengue fever is a typical mosquito-borne infectious disease, and four strains of it are currently found. Clinical medical research has shown that the infected person can provide life-long immunity against the strain after recovering from infection with one strain, but only provide partial and temporary immunity against other strains. On the basis of the complexity of transmission and the diversity of pathogens, in this paper, a multi-strain dengue transmission model with latency age and cross immunity age is proposed. We discuss the well-posedness of this model and give the terms of the basic reproduction number R-0 = max{R-1, R-2}, where R-i is the basic reproduction number of strain i (i = 1, 2). Particularly, we obtain that the model always has a unique disease-free equilibrium P-0 which is locally stable for R-0 < 1. And same time, an explicit condition of the global asymptotic stability of P-0 is obtained by constructing a suitable Lyapunov functional. Furthermore, we also shown that if R-i > 1, the strain-i dominant equilibrium P-i is locally stable for R-j < R-i* (i, j = 1, 2, i not equal j). Additionally, the threshold criteria on the uniformly persistence, the existence and global asymptotically stability of coexistence equilibrium are also obtained. Finally, these theoretical results and interesting conclusions are illustrated with some numerical simulations.Keywords
This publication has 40 references indexed in Scilit:
- Threshold dynamics of a malaria transmission model in periodic environmentCommunications in Nonlinear Science and Numerical Simulation, 2013
- The global distribution and burden of dengueNature, 2013
- Transmission Dynamics of the Four Dengue Serotypes in Southern Vietnam and the Potential Impact of VaccinationPLOS ONE, 2012
- COEXISTENCE OF THE STRAINS INDUCED BY MUTATIONInternational Journal of Biomathematics, 2012
- Backward bifurcations in dengue transmission dynamicsMathematical Biosciences, 2008
- Destabilizing effect of the host immune status on the sequential transmission dynamic of the dengue virus infectionMathematical and Computer Modelling, 2007
- Dengue fever: Mathematical modelling and computer simulationApplied Mathematics and Computation, 2006
- Global Attractors and Steady States for Uniformly Persistent Dynamical SystemsSIAM Journal on Mathematical Analysis, 2005
- How May Infection-Age-Dependent Infectivity Affect the Dynamics of HIV/AIDS?SIAM Journal on Applied Mathematics, 1993
- Persistence in Infinite-Dimensional SystemsSIAM Journal on Mathematical Analysis, 1989