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In this paper, we formulated a new nine (9) compartmental mathematical model to have better understanding of parameters that influence the dynamical spread of Human immunodeficiency virus (HIV) interacting with Tuberculosis (TB) in a population. The model is analyzed for all the parameters responsible for the disease spread in order to find the most sensitive parameters out of all. Sub models of HIV and TB only were considered first, followed by the full HIV-TB co-infection model. Stability of HIV model only, TB model only and full model of HIV-TB co-infection were analyzed for the existence of the disease free and endemic equilibrium points.  Basic Reproduction Number (R0) was obtained using next generation matrix method (NGM), and it has been shown that the disease free equilibrium point is locally asymptotically stable whenever R0 > 1and unstable whenever this threshold exceeds unity. i.e.. R0 > 1 The relative sensitivity solutions of the model with respect to each of the parameters is calculated, Parameters are grouped into two categories: sensitive parameters and insensitive parameters. Numerical simulation was carried out by maple software using Runge-kunta method, to show the effect of each parameter on the dynamical spread of HIV-TB co-infection, i.e. detection of infected undetected individuals plays a vital role, it decreases infected undetected individuals. Also, increased in effective contact rate has a pronounced effect on the total population; it decreases susceptible individuals and increases the infected individuals. However, effective contact rate needs to be very low in order to guaranteed disease free environment.

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Human Immunodeficiency Virus (HIV) co-existing with Tuberculosis (TB) in individuals remains a major global health challenges, with an estimated 1.4 million patients worldwide. These two diseases are enormous public health burden, and unfortunately, not much has been done in terms of modeling the dynamics of HIV-TB co-infection at a population level. We formulated new fifteen (15) compartmental models to gain more insight into the effect of treatment and detection of infected undetected individuals on the dynamical spread of HIV- TB co-infection. Sub models of HIV and TB only were considered first, followed by the full HIV-TB co-infection model. Existence and uniqueness of HIV and TB only model were analyzed quantitatively, and we shown that HIV model only and TB only model have solutions, moreover, the solutions are unique. Stability of HIV model only, TB model only and full model of HIV-TB co-infection were analyzed for the existence of the disease free and endemic equilibrium points. Basic reproduction number () was analyzed, using next generation matrix method (NGM), and it has been shown that the disease free equilibrium point is locally asymptotically stable whenever  and unstable whenever this threshold exceeds unity. i.e., Numerical simulation was carried out by maple software using differential transformation method, to show the effect of  treatment and detection of infected undetected individuals on the dynamical spread of HIV-TB co-infection. Significantly, all the results obtained from this research show the importance of treatment and detection of infected undetected individuals on the dynamical spread of HIV-TB co-infection. Detection rate of infected undetected individuals reduce the spread of HIV-TB co-infections.