Dynamics model analysis of bacteriophage infection of bacteria

A bacteriophage (in short, phage) is a virus that can infect and replicate within bacteria. Assuming that uninfected and infected bacteria are capable of reproducing with logistic law, we investigate a model of bacteriophage infection that resembles simple SI-models widely used in epidemiology. The dynamics of host-parasite co-extinctions may exhibit four scenarios: hosts and parasites go extinct, parasites go extinct, hosts go extinct, and hosts and parasites coexist. By using the Jacobian matrix and Bendixson–Dulac theory, local and global stability analysis of uninfected and infected steady states is provided; the basic reproduction number of the model is given; general results are supported by numerical simulations. We show that bacteriophages can reduce a host density. This provides a theoretical framework for studying the problem of whether phages can effectively prevent, control, and treat infectious diseases.

Local and Global Stability Analysis of Dengue Disease with Vaccination and Optimal Control

Dengue fever is a disease that has spread all over the world, including Thailand. Dengue is caused by a virus and there are four distinct serotypes of the virus that cause dengue DENV-1, DENV-2, DENV-3, and DENV-4. The dengue viruses are transmitted by two species of the Aedes mosquitoes, the Aedes aegypti, and the Aedes albopictus. Currently, the dengue vaccine used in Thailand is chimeric yellow tetravalent dengue (CYD-TDV). This research presents optimal control which studies the vaccination only in individuals with a documented past dengue infection (seropositive), regardless of the serotypes of infection causing the initial infection by the disease. The analysis of dengue transmission model is used to establish the local asymptotically stabilities. The property of symmetry in the Lyapunov function an import role in achieving this global asymptotically stabilities. The optimal control systems are shown in numerical solutions and conclusions. The result shows that the control resulted in a significant reduction in the number of infected humans and infected vectors.

On the Global Stability Analysis of Corona Virus Disease (COVID-19) Mathematical Model

In this present work, we investigated the Global Stability Analysis of Corona virus disease model formulated by Atokolo et al in [11]. The COVID‑19 pandemic, also known as the coronavirus pandemic, is an ongoing pandemic that is ravaging the whole world. By constructing a Lyapunov function, we investigated the stability of the model Endemic Equilibrium state to be globally asymptotically stable. This results epidemiologically implies that the COVID-19 will invade the population in respective of the initial conditions (population) considered.