Dengue fever

Biology

Differential equation

Applied mathematics

Virology

Stability (learning theory)

Telecommunications

Economics

Computer science

Integer (computer science)

Mathematics

Stability theorem

Attractor

Mathematical analysis

Ordinary differential equation

Cauchy distribution

Combinatorics

Transmission (telecommunications)

Programming language

Partial differential equation

Finance

Order (exchange)

Machine learning

Advances in Difference Equations

A non-linear mathematical model with non-integer order γ, $0 < \gamma \leq 1$ , is used to analyze the dengue virus transmission in the human body. Both disease-free $\mathcal{F}_{0}$ and endemic $\mathcal{F}^{*}$ equilibria are calculated. Their stability is also described using the stability theorem of non-integer order. The threshold parameter $\mathcal{R}_{0}$ demonstrates an important behavior in the stability of a considerable model. For $\mathcal{R}_{0} < 1$ , the disease-free equilibrium (DFE) $\mathcal{F}_{0}$ is an attractor. For $\mathcal{R}_{0} > 1$ , $\mathcal{F}_{0}$ is not stable, the endemic equilibrium (EE) $\mathcal{F}^{*}$ exists, and it is an attractor. Numerical examples of the proposed model are also proven to study the behavior of the system.

A non-integer order dengue internal transmission model