On mathematical model of the impact of non-compliance with preventive measures for the prevention of the spread of HIV/AIDS among heterogeneous population - Статья

On mathematical model of the impact of non-compliance with preventive measures for the prevention of the spread of hiv/aids among heterogeneous population INTRODUCTION The basic routes of the Human Immune Deficiency Virus (HIV) transmission between persons are now well understood and widely known, but the non-adherent to the application of recommended preventive measures which leads to HIV prevalence and trends among population has remained an area of debate and scientific research [1]. Diseases can be transmitted either horizontally or vertically. In the case of HIV, horizontal transmission occurs from direct contact between an infected individual and susceptible persons. Vertical transmission is as a result of direct transfer from mother-to-child or newborn offspring [2], as over 40% of all HIV cases result from mother-to-child transmission. The Human Immune Deficiency Virus (HIV) is known to be the causative agent of the deadly disease called the Acquired Immune Deficiency Syndrome (AIDS), the extensive spread of which appears to have commenced in the early 1980s, [3]. In sub-Saharan Africa, over 2.5 million children under the age of 15, have died of AIDS as a result of been exposed to HIV during labor or breastfeeding. Thus, the impact of HIV transmission has been felt mainly in Africa [4], where the level of literacy is low, the poverty level is very high and the quality of health services is generally very poor. The dynamics of HIV/AIDS has moved beyond the virus and risk factors associated with its transmission to a more detailed understanding of the mechanisms associated with the spread, distribution and impact of any intervention on the population [5]. Transmission modes of HIV/AIDS are basically via heterosexual contacts, blood transfusion, and contaminated injecting equipment [6]. Due to non-availability of any known medical cure for HIV/AIDS, therapeutic treatment strategies appear promising for retarding the progression of HIV-related diseases. In other words, prevention has remained the most effective strategy against the HIV/AIDS epidemics [7]. Control and intervention programs are focused towards educating the people on behavioral change. Other method of control include barrier contraceptives (i.e. condom use), which is a single strategy in the prevention of HIV/AIDS. Condom use, as a strategy to halt the HIV epidemics is considered in terms of its efficacy and compliance. The study of these two factors has been more rewarding through mathematical modeling. Mathematical models of the transmission of HIV have proven to be useful in providing a logical structure within which to incorporate knowledge and test assumptions about the complex HIV epidemic [8]. Through mathematical modeling, the control of HIV/AIDS have been formulated as far back as 1987, when [9], developed simple function for the growth in the number of individuals who will develop AIDS and for the distribution of incubation period of those individuals [10]. Other models for the control of HIV epidemic include the following aspects: age-structure population, differential infectivity and stage progression; fully-integrated immune response model (FIRM), defense model, random screening, contact tracing, use of condom etc., for example, see [5,8,10,11,12, 13,14,15,16,17]. The motivating factor of this present work lies in the model [10], on a two-sex mathematical model for the prevention of the spread of HIV/AIDS in a varying population. In that study, the preventive measure (condom use) was, as well, introduced to the susceptible males among others. 1(a & b): A flow-chat of the model for male and female population for the prevention of HIV/AIDS in different groups of the population. From figure 1(a), the functions (parameters) used in the model for the male populations are as defined below: Sm(t) - Number of susceptible males at time t; Im(t) - Number of infected males at time t; Wm(t) - Number of infected males who use the condom at time t; Um(t) - Number of susceptible males who use the condom at time t; Nm(t) - Total population of males at time t; Bm(t) - The rate at which males are infected per unit time (incident rate); bNm - Natural birth rate of male population, ; µ - Natural death rate, ; ? - AIDS - related death rate, ; ?1 - The proportion of infected males who use the condom per unit time; ?2 - The proportion of infected males who initially use the condom and then decline per unit time; s1 - The proportion of susceptible males who use the condom per unit time; s2 - The proportion of susceptible males who initially use the condom and then decline per unit time; сm - Average number of contacts by males with females per unit time; ?m - Probability of transmission by an infected males; and ?m* - Probability of transmission by an infected males who use the condom. Where Using figure (1b), we also derive the functions (parameters) used in the model for the female population: Sf(t) - Number of susceptible females at time t; I