Mathematical modeling of transmission co-infection tuberculosis in HIV community

TB and HIV infection have the effect of deeply on assault the immune system, since they can afford to weaken host immune respone through a mechanism that has not been fully understood. HIV co-infection is the stongest risk factor for progression of M. tuberculosis to active TB disease in HIV individuals, as well as TB has been accelerated to progression HIV infection. In this paper we create a model of transmission co-infection TB in HIV community, dynamic system with ten compartments built in here. Dynamic analysis in this paper mentioned ranging from disease free equilibrium conditions, endemic equilibrium conditions, basic reproduction ratio, stability analysis and numerical simulation. Basic reproductive ratio were obtained from spectral radius the next generation matrix of the model. Numerical simulations are built to justify the results of the analysis and to see the changes in the dynamics of the population in each compartment. The sensitivity analysis indicates that the parameters affecting the population dynamics of TB in people with HIV infection is parameters rate of progression of individuals from the exposed TB class to the active TB, treatment rate of exposed TB individuals, treatment rate of infectious (active TB) individuals and probability of transmission of TB infection from an infective to a susceptible per contact per unit time. We can conclude that growing number of infections carried by infectious TB in people with HIV infection can lead to increased spread of disease or increase in endemic conditions.