Bifurcation study of a tumor-immune system with chemotherapy.

Understanding the dynamics of cancer cell growth, the interplay between tumor and immune cells, and the efficacy of chemotherapy are pivotal areas of focus in cancer research. In this regard, mathematical modeling can provide significant insights. This study re-examines a classical two-dimensional model of tumor-immune cell interactions where the tumor's growth rate is assumed to adhere to von Bertalanffy's model instead of the logistic model.

Analysis and comparative study of a deterministic mathematical model of SARS-COV-2 with fractal-fractional operators: a case study.

In this paper, we investigate a fractal-fractional-order mathematical model with the influence of hospitalized patients and the impact of vaccination with fractal-fractional operators. The respective derivatives are considered in the Caputo, Caputo Fabrizio, and Atangana-Baleanu senses of fractional order and fractal dimension . For the proposed problem, some results regarding basic reproduction number and stability are given.

Unravelling the dynamics of the COVID-19 pandemic with the effect of vaccination, vertical transmission and hospitalization.

The coronavirus disease 2019 (COVID-19) is caused by a newly emerged virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), transmitted through air droplets from an infected person. However, other transmission routes are reported, such as vertical transmission. Here, we propose an epidemic model that considers the combined effect of vertical transmission, vaccination and hospitalization to investigate the dynamics of the virus's dissemination.

Bifurcation analysis of a SEIR epidemic system with governmental action and individual reaction.

In this paper, the dynamical behavior of a SEIR epidemic system that takes into account governmental action and individual reaction is investigated. The transmission rate takes into account the impact of governmental action modeled as a step function while the decreasing contacts among individuals responding to the severity of the pandemic is modeled as a decreasing exponential function. We show that the proposed model is capable of predicting Hopf bifurcation points for a wide range of physically realistic parameters for the COVID-19 disease.

An efficient numerical algorithm for solving fractional SIRC model with salmonella bacterial infection.

This paper revisits the study of numerical approaches for fractional SIRC model with Salmonella bacterial infection (FSIRC-MSBI). This model is investigated by the aid of fully shifted Jacobi's collocation method for temporal discretization. It is concluded that the method of the current paper is far more efficient and reliable for the considered model.