naresh1

Title

Modelling and analysis of HIV TB co infection in a variable size population

Authors

R. Naresh (a) and A. Tripathi (b)

Affiliations

a) Department of Mathematics, Harcourt Butler Technological Institute, Kanpur, Uttar Pradesh, 208002, India E-mail: b) Department of Mathematics, Harcourt Butler Technological Institute, Kanpur, Uttar Pradesh, 208002, India

Abstract

In this paper, a nonlinear mathematical model is proposed for the transmission dynamics of HIV and a curable TB pathogen within a population of varying size. In the model, we have divided the population into four sub classes of susceptibles, TB infectives, HIV infectives and that of AIDS patients. The model exhibits four equillibria namely, a disease free, HIV free, TB free and a co‐infection equilibrium. The model has been studied qualitatively using stability theory of nonlinear differential equations. It is shown that the positive co‐infection equilibrium is always locally stable but it may become globally stable under certain conditions showing that the disease becomes endemic due to constant migration of the population into the habitat. A numerical study of the model is also performed to investigate the influence of certain key parameters on the spread of the disease.

Journal

Mathematical Modelling and Analysis. Volume 10, Issue 3, 2005.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Global parameters

Local parameters

Assignment rules

Rate rules

Algebraic rules