Stochastic two-strain epidemic model with saturated incidence rates driven by Lévy noise.

In this paper, we introduce a stochastic two-strain epidemic model driven by Lévy noise describing the interaction between four compartments; susceptible, infected individuals by the first strain, infected ones by the second strain and the recovered individuals. The forces of infection, for both strains, are represented by saturated incidence rates. Our study begins with the investigation of unique global solution of the suggested mathematical model.

Local and global stability of an HCV viral dynamics model with two routes of infection and adaptive immunity.

The aim of this article is to formulate and study a mathematical model describing hepatitis C virus (HCV) infection dynamics. The model includes two essential modes of infection transmission, namely, virus-to-cell and cell-to-cell. The effect of therapy and adaptive immunity are incorporated in the suggested model.

Modelling disease spread with spatio-temporal fractional derivative equations and saturated incidence rate.

The global analysis of a spatio-temporal fractional order SIR infection model with saturated incidence function is suggested and studied in this paper. The dynamics of the infection is described by three partial differential equations including a time-fractional derivative order for each one of them. The equations of our model describe the evolution of the susceptible, the infected and the recovered individuals with taking into account the spatial diffusion for each compartment.

On a two-strain epidemic mathematical model with vaccination.

In this paper, we study mathematically a two strains epidemic model taking into account non-monotonic incidence rates and vaccination strategy. The model contains seven ordinary differential equations that illustrate the interaction between the susceptible, the vaccinated, the exposed, the infected and the removed individuals. The model has four equilibrium points, namely, disease free equilibrium, endemic equilibrium with respect to the first strain, endemic equilibrium with respect to the second strain and the endemic equilibrium with respect to both strains.

Hepatitis C virus fractional-order model: mathematical analysis.

Mathematical analysis of epidemics is crucial for the prediction of diseases over time and helps to guide decision makers in terms of public health policy. It is in this context that the purpose of this paper is to study a fractional-order differential mathematical model of HCV infection dynamics, incorporating two fundamental modes of transmission of the infection; virus-to-cell and cell-to-cell along with a cure rate of infected cells. The model includes four compartments, namely, the susceptible hepatocytes, the infected ones, the viral load and the humoral immune response, which is activated in the host to attack the virus.

Theoretical and numerical results of a stochastic model describing resistance and non-resistance strains of influenza.

In this world, there are several acute viral infections. One of them is influenza, a respiratory disease caused by the influenza virus. Stochastic modelling of infectious diseases is now a popular topic in the current century.

A fractional-order model of coronavirus disease 2019 (COVID-19) with governmental action and individual reaction.

The deadly coronavirus disease 2019 (COVID-19) has recently affected each corner of the world. Many governments of different countries have imposed strict measures in order to reduce the severity of the infection. In this present paper, we will study a mathematical model describing COVID-19 dynamics taking into account the government action and the individuals reaction.

Stability analysis and optimal control of HPV infection model with early-stage cervical cancer.

Cervical cancer cells may develop from any cell infected by human papillomavirus (HPV). The aim of this paper is to study whether an optimal control of HPV infection can reduce those resulting cancer cells. To this end, the problem will be modelled by five differential equations that describe the interactions between healthy cells, infected cells, free virus, precancerous cells and cancer cells.

Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic.

This paper investigates the global stability analysis of two-strain epidemic model with two general incidence rates. The problem is modelled by a system of six nonlinear ordinary differential equations describing the evolution of susceptible, exposed, infected and removed individuals. The wellposedness of the suggested model is established in terms of existence, positivity and boundedness of solutions.

Mathematical Analysis and Clinical Implications of an HIV Model with Adaptive Immunity.

In this paper, a mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with adaptive immune response is presented and studied. The mathematical model includes six nonlinear differential equations describing the interaction between the uninfected cells, the exposed cells, the actively infected cells, the free viruses, and the adaptive immune response. The considered adaptive immunity will be represented by cytotoxic T-lymphocytes cells (CTLs) and antibodies.

Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids.

We model the transmission of the hepatitis B virus (HBV) by six differential equations that represent the reactions between HBV with DNA-containing capsids, the hepatocytes, the antibodies and the cytotoxic T-lymphocyte (CTL) cells. The intracellular delay and treatment are integrated into the model. The existence of the optimal control pair is supported and the characterization of this pair is given by the Pontryagin's minimum principle.

Prediction of DNA methylation in the promoter of gene suppressor tumor.

The epigenetics methylation of cytosine is the most common epigenetic form in DNA sequences. It is highly concentrated in the promoter regions of the genes, leading to an inactivation of tumor suppressors regardless of their initial function. In this work, we aim to identify the highly methylated regions; the cytosine-phosphate-guanine (CpG) island located on the promoters and/or the first exon gene known for their key roles in the cell cycle, hence the need to study gene-gene interactions.