Abstract
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.
Highlights
INTRODUCTION1.1 Human Immunodeficiency Virus (HIV) is the etiological agent that causes acquired Immunodeficiency
1.1 Human Immunodeficiency Virus (HIV) is the etiological agent that causes acquired ImmunodeficiencySyndrome (AIDS) when left untreated
This work deals with the formulation and analysis of mathematical model to have better understanding of detection of infected undetected individuals and treatment strategies on the dynamical spread of HIV-TB co-infection
Summary
1.1 Human Immunodeficiency Virus (HIV) is the etiological agent that causes acquired Immunodeficiency. The population of latent TB induced HIV is increased by infection, which can be acquired following effective contact with infections individuals in the latent TB induced HIV ( LTH ), Active TB induced HIV ( T ATH ) or Recovered TB induced HIV ( RT RTH ) categories at a rate given by (11). The population of active TB induced HIV is increased by the progression from latent stage to active stage at the rate ( TH ), the population decreased by natural death, induced mortality due to disease at the rate ( ) and ( ) respectively, individual who recovered moved to recovered TB induced HIV at the rate ( 1 ). The population of latent HIV induced TB is increased by infection, which can be acquired following effective contact with infectious individuals in the latent HIV induced TB (LHT ) , or active HIV induced TB ( H AHT ) categories at a rate given by (14). Detected individuals who are successfully treated HIV-induced mortality rate for classes HU , H D respectively HIV Modification parameters for classes HU , H D , HW respectively TB Modification parameters for classes TU ,TD , FT , RT respectively
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