Analysis and optimal control of an HIV model based on CD4 count.

A non-linear mechanistic model for the transmission dynamics of HIV/AIDS is developed and analyzed. The model classified the infected individuals based on their CD4 count level. Furthermore, education campaign, voluntary testing and counseling and treatment are considered as intervention strategies for controlling the disease. The analysis of the model reveals that imperfect public enlightenment campaign can induce backward bifurcation. It has been shown that when public enlightenment campaign is [Formula: see text] effective, the disease free equilibrium is globally asymptotically stable for [Formula: see text], whereas for [Formula: see text] the global stability of the endemic equilibrium is proved only in a special case. Time dependent controls of the intervention strategies mentioned above are incorporated into the model and the optimal control strategies with minimal implementation cost are identified. In addition, cost effectiveness analysis in the form of incremental cost effectiveness ratio is carried-out to identify the most cost effective strategies. The results suggest that out of the three non dominated strategies, the strategy of educating the newly entrants only or combination of newly entrants and susceptible individuals is very cost effective using per capita GDP of Nigeria as at 2018. However, the choice of which strategy to implement depends on budgetary allocation and resource availability.

Mathematical analysis of a model for AVL-HIV co-endemicity.

A model for the transmission dynamics of Anthroponotic Visceral Leishmaniasis (AVL) and human immunodeficiency virus (HIV) in a population is developed and used to assess the impact of the spread of each disease on the overall transmission dynamics. As for other vector-borne disease models, the AVL component of the model undergoes backward bifurcation when the associated reproduction number of the AVL-only sub-model (denoted by RL) is less than unity. Uncertainty and sensitivity analyzes of the model, using data relevant to the dynamics of the two diseases in Ethiopia, show that the top three parameters that drive the AVL infection (with respect to the associated response function, RL) are the average number of times a sandfly bites humans per unit time (σV), carrying capacity of vectors (KV) and transmission probability from infected humans to susceptible sandflies (ß2). The distribution of RL is RL∈[0.06,3.94] with a mean of RL=1.08. Furthermore, the top three parameters that affect HIV dynamics (with respect to the response function RH) are the transmission rate of HIV (ßH), HIV-induced death rate (δH), and the modification parameter for the increase in infectiousness of AIDS individuals in comparison to HIV infected without clinical symptoms of AIDS (ωH). The distribution of RH is RH∈[0.88,2.79] with a mean of RH=1.46. The dominant parameters that affect the dynamics of the full VL-HIV model (with respect to the associated reproduction number, RLH, as the response function) are the transmission rate of HIV (ßH), the average number of times a sandfly bites humans per unit time (σV), and HIV-induced death rate (δH) (the distribution of RLH is RLH∈[0.88,3.94] with a mean of RLH=1.64). Numerical simulations of the model show that the two diseases co-exist (with AVL dominating, but not driving HIV to extinction) whenever the reproduction number of each disease exceeds unity. It is shown that AVL can invade a population at HIV-endemic state if a certain threshold quantity, known as invasion reproduction number, exceeds unity.

Qualitative assessment of the role of public health education program on HIV transmission dynamics.

This paper presents a non-linear deterministic model for assessing the impact of public health education campaign on curtailing the spread of the human immunodeficiency virus (HIV) pandemic in a population. Rigorous qualitative analysis of the model reveals that it exhibits the phenomenon of backward bifurcation (BB), where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the 'effective reproduction number' ('Reff), is less than unity. The epidemiological implication of BB is that a public health education campaign could fail to effectively control HIV even when the classical requirement of having the associated reproduction number less than unity is satisfied. Furthermore, an explicit threshold value is derived above which such an education campaign could lead to detrimental outcome (increase disease burden) and below which it would have positive population-level impact (reduce disease burden in the community). It is shown that the BB phenomenon is caused by imperfect efficacy of the public health education program. The model is used to assess the potential impact of some targeted public health education campaigns using data from numerous countries.