Qualitative analysis of generalized multistage epidemic model with immigration.

A model with multiple disease stages is discussed; its main feature is that it considers a general incidence rate, functions for death and immigration rates in all populations. We show via a suitable Lyapunov function that the unique endemic equilibrium is globally asymptotically stable. We conclude that, in order to obtain the existence and global stability of the equilibrium point of general models, conditions must be imposed on the functions present in the model.

Mathematical model of interaction and Coliphages.

We propose a mathematical model based in ordinary differential equations between bacterial pathogen and Bacteriophages to describe the infection dynamics of these populations, for which we use a nonlinear function with an inhibitory effect. We study the stability of the model using the Lyapunov theory and the second additive compound matrix and perform a global sensitivity analysis to elucidate the most influential parameters in the model, besides we make a parameter estimation using growth data of bacteria in presence of Coliphages (bacteriophages that infect ) with different multiplicity of infection. We found a threshold that indicates whether the bacteriophage concentration will coexist with the bacterium (the coexistence equilibrium) or become extinct (phages extinction equilibrium), the first equilibrium is locally asymptotically stable while the other is globally asymptotically stable depending on the magnitude of this threshold.

Global stability analysis for a model with carriers and non-linear incidence rate.

We analysed a epidemiological model with varying populations of susceptible, carriers, infectious and recovered (SCIR) and a general non-linear incidence rate of the form [Formula: see text]. We show that this model exhibits two positive equilibriums: the disease-free and disease equilibrium. We proved using the Lyapunov direct method that these two equilibriums are globally asymptotically stable under some sufficient conditions over the functions , , .

Mathematical modelling of MS2 virus inactivation by Al/Fe-PILC-activated catalytic wet peroxide oxidation (CWPO).

Catalytic wet peroxide oxidation (CWPO) is a novel, alternative technology to conventional disinfection methods that are widely used to control microbial parameters in drinking water. To assess its effectiveness, new studies revealing the kinetics of MS2 coliphage inactivation by CWPO technology are required. This investigation therefore aimed to perform mathematical modelling of MS2 inactivation through CWPO technology activated by an Al/Fe-pillared clay catalyst (Al/Fe-PILC) in the presence of a synthetic surrogate of dissolved natural organic matter.

Mathematical model for the growth of Mycobacterium tuberculosis in the granuloma.

In this work we formulate a model for the population dynamics of Mycobacterium tuberculosis (Mtb), the causative agent of tuberculosis (TB). Our main interest is to assess the impact of the competition among bacteria on the infection prevalence. For this end, we assume that Mtb population has two types of growth.

Mathematical modeling on bacterial resistance to multiple antibiotics caused by spontaneous mutations.

We formulate a mathematical model that describes the population dynamics of bacteria exposed to multiple antibiotics simultaneously, assuming that acquisition of resistance is through mutations due to antibiotic exposure. Qualitative analysis reveals the existence of a free-bacteria equilibrium, resistant-bacteria equilibrium and an endemic equilibrium where both bacteria coexist.

On the interactions of sensitive and resistant Mycobacterium tuberculosis to antibiotics.

In this work we propose a system of non linear ordinary differential equations for the dynamics of Mycobacterium tuberculosis (Mtb) within the host, in order to study the role of macrophages, T cells and antibiotics in the control of sensitive and resistant Mtb. Conditions for the persistence of sensitive and resistant bacteria are given in terms of the secondary infections produced by bacteria and macrophages, the immune response, and the antibiotic treatment. Model analysis predicts backward bifurcations for certain values of the parameters.

A mathematical model for cellular immunology of tuberculosis.

Tuberculosis (TB) is a global emergency. The World Health Organization reports about 9.2 million new infections each year, with an average of 1.