36 documents found, page 1 of 4

International Conference Mathematical Analysis and Applications in Science and ...

Hands-on and remote lab in an engineering statistics course

A latency fractional order model for HIV dynamics

We study a fractional order model for HIV infection where latent T helper cells are included. We compute the reproduction number of the model and study the stability of the disease free equilibrium. We observe that the reproduction number varies with the order of the fractional derivative α. In terms of epidemics, this suggests that varying α induces a change in the patients’ epidemic status. Moreover, we simul...

Persistence of low levels of plasma viremia and of the latent reservoir in pati...

Low levels of viral load are found in HIV-infected patients, after many years under successful suppressive anti-retroviral therapy (ART). The factors leading to this persistence are still under debate, but it is now more or less accepted that the latent reservoir may be crucial to the maintenance of this residual viremia. In this paper, we study the role of the latent reservoir in the persistence of the latent ...

A note on fractional feed-forward networks

We simulate a fractional feed-forward network. This network consists of three coupled identical ‘cells’ (aka, oscillators). We study the behaviour of the associated coupled cell system for variation of the order of the fractional derivative, 0 < α < 1. We consider the Caputo derivative, approximated by the Grünwald–Letnikov approach, using finite differences of fractional order. There is observed amplification ...

Strange patterns in one ring of Chen oscillators coupled to a ‘buffer’ cell

We study curious dynamical patterns appearing in networks of one ring of cells coupled to a ‘buffer’ cell. Depending on how the cells in the ring are coupled to the ‘buffer’ cell, the full network may have a nontrivial group of symmetries or a nontrivial group of ‘interior’ symmetries. This group is Z3 in the unidirectional case and D3 in the bidirectional case. We simulate the coupled cell systems associated w...

Within-host and synaptic transmissions: contributions to the spread of HIV infe...

We study the contributions of within-host (virus-to-cell) and synaptic (cell-to-cell) transmissions in a mathematical model for human immunodeficiency virus epidemics. The model also includes drug resistance. We prove the local and global stability of the disease-free equilibrium and the local stability of the endemic equilibrium. We analyse the effect of the cell-to-cell transmission rate on the value of the r...

Fractional complex-order model for HIV infection with drug resistance during th...

We propose a fractional complex-order model for drug resistance in HIV infection. We consider three distinct growth rates for the CD4+ T helper cells. We simulate the model for different values of the fractional derivative of complex order Dα±jβ, where α,β ∈ R+, and for distinct growth rates. The fractional derivative of complex order is a generalization of the integer-order derivative where α = 1 and β = 0. Th...

Coupled fractional spiking neurons

We propose a fractional-order (FO) model of two symmetrically coupled Hodgkin-Huxley equations and study the patterns of the neurons’ firing rates, for distinct values of the order of the fractional derivative, , and the temperature, . We find that, for positive values of the coupling, the neurons exhibit in-phase periodic solutions (neurons fire at the same time). Moreover, the spike amplitude decreases with ,...

Emergence of drug-resistance in HIV dynamics under distinct HAARTregimes

In this paper we propose a model for the dynamics of HIV epidemics under distinct HAART regimes, and study the emergence of drug-resistance. The model predicts HIV dynamics of untreated HIV patients for all stages of the infection. We compute the local and the global stability of the disease-free equilibrium of the model. We simulate the model for two distinct HIV patients, the rapid progressors and the long-te...