Dynamics model analysis of bacteriophage infection of bacteria

Abstract

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.

Modeling the effect of contaminated object, vaccination and treatment on the diseases epidemiology

“…This humanity effort to prevent the spreading infectious disease cannot be well done only by biological and healthcare. Mathematical modeling of the infectious diseases is one of the key tools in order to handle these efforts [7][8][9][10] .…”