## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

MBE

Infection age is an important factor affecting the transmission of
infectious diseases. In this paper, we consider an SIRS model
with infection age, which is described by a mixed system of
ordinary differential equations and partial differential
equations. The expression of the basic reproduction number
$\mathscr {R}_0$ is obtained. If $\mathscr{R}_0\le 1$ then the
model only has the disease-free equilibrium, while if
$\mathscr{R}_0>1$ then besides the disease-free equilibrium the
model also has an endemic equilibrium. Moreover, if
$\mathscr{R}_0<1$ then the disease-free equilibrium is globally
asymptotically stable otherwise it is unstable; if
$\mathscr{R}_0>1$ then the endemic
equilibrium is globally asymptotically stable under additional conditions. The local stability
is established through linearization. The global stability of the
disease-free equilibrium is shown by applying the fluctuation
lemma
and that of the endemic equilibrium is proved by employing Lyapunov functionals.
The theoretical results are illustrated with numerical simulations.

DCDS-B

In this paper, a two-strain epidemic model on a complex network is proposed. The two strains are the drug-sensitive strain and the drug-resistant strain. The related basic reproduction numbers $R_s$ and $R_r$ are obtained. If $R_0=\max\{R_s,R_r\}<1$, then the disease-free equilibrium is globally asymptotically stable. If $R_r>1$, then there is a unique drug-resistant strain dominated equilibrium $E_r$, which is locally asymptotically stable if the invasion reproduction number $R_r^s<1$. If $R_s>1$ and $R_s>R_r$, then there is a unique coexistence equilibrium $E^*$. The persistence of the model is also proved. The theoretical results are supported with numerical simulations.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]