A Model for Control of Hiv/Aids With Parental Care

Abiodun, Gbenga J.; Marcus, Nizar; Okosun, Kazeem Oare; Witbooi, Peter J.

doi:10.1142/s179352451350006x

Cited by 12 publications

(9 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All the diseased classes of human and chimpanzees are equal to zero. () Therefore, the D F E of the model system is obtained as

E^{*} = ((), S_{h}^{*}, R_{h}^{*}, I_{1}^{*}, I_{2}^{*}, A_{h}^{*}, S_{c}^{*}, I_{c}^{*}, A_{c}^{*}) = ((), \frac{π_{h}}{false(μ_{h} + τ false)}, \frac{τ π_{h}}{μ_{h} false(μ_{h} + τ false)}, 0, 0, 0, \frac{π_{c}}{μ_{c}}, 0, 0) .

…”

Section: Basic Properties Of Siv→hiv Modelmentioning

confidence: 99%

“…All the diseased classes of human and chimpanzees are equal to zero. 15,31 Therefore, the DFE of the model system (3) is obtained as…”

Section: Disease-free Equilibriummentioning

confidence: 99%

“…On the basis of the analysis of the model, they show that constant immigration of H I V ‐infected individuals leads to the endemicity of the disease. Abiodun et al have studied a mathematical model examining the effects of parental care in the presence of infected immigrants. Model analysis reveals that the model does not have disease‐free equilibrium ( D F E ) point when there is continuous immigration of infective youths.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal control and sensitivity analysis of SIV→HIV dynamics with effects of infected immigrants in sub‐Saharan Africa

Sule

Abdullah

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

Regional migration has become an underlying factor in the spread of HIV transmission. In addition, immigrants with HIV status has contributed with high‐risk of sexually transmitted infection to its “destination” communities and promotes dissemination of HIV. Efforts to address HIV/AIDS among conflict‐affected populations should be properly addressed to eliminate potential role of the spread of the disease and risk of exposure to HIV. Motivated from this situation, HIV‐infected immigrants factor to HIV/SIV transmission link will be investigated in this research and examine its potential effect using optimal control method. Nonlinear deterministic mathematical model is used which is a multiple host model comprising of humans and chimpanzees. Some basic properties of the model such as invariant region and positivity of the solutions will be examined. The local stability of the disease‐free equilibrium was examined by computing the basic reproduction number, and it was found to be locally asymptotically stable when ℜ0<1 and unstable otherwise. Sensitivity analysis was conducted to determine the parameters that help most in the spread of the virus. Pontryagin's maximum principle is used to obtain the optimality conditions for controlling the disease spread. Numerical simulation was conducted to obtain the analytical results. The results shows that combination of public health awareness, treatment, and culling help in controlling the HIV disease spread.

show abstract

“…All the diseased classes of human and chimpanzees are equal to zero. () Therefore, the D F E of the model system is obtained as

E^{*} = ((), S_{h}^{*}, R_{h}^{*}, I_{1}^{*}, I_{2}^{*}, A_{h}^{*}, S_{c}^{*}, I_{c}^{*}, A_{c}^{*}) = ((), \frac{π_{h}}{false(μ_{h} + τ false)}, \frac{τ π_{h}}{μ_{h} false(μ_{h} + τ false)}, 0, 0, 0, \frac{π_{c}}{μ_{c}}, 0, 0) .

…”

Section: Basic Properties Of Siv→hiv Modelmentioning

confidence: 99%

“…All the diseased classes of human and chimpanzees are equal to zero. 15,31 Therefore, the DFE of the model system (3) is obtained as…”

Section: Disease-free Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal control and sensitivity analysis of SIV→HIV dynamics with effects of infected immigrants in sub‐Saharan Africa

Sule

Abdullah

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Here we derive the sensitivity index by using partial rank correlation coefficients (PRCCs) of the basic reproductive ratio with respect to the parameters. According to Abiodun et al (2013), the normalized forward sensitivity index of R 0 with respect to a parameter m is defined as follows:…”

Section: 1mentioning

confidence: 99%

A Comparative Study Between Two Systems with and Without Awareness in Controlling HIV/AIDS

Saha

Roy

2017

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

It has always been a priority for all nations to reduce new HIV infections by implementing a comprehensive HIV prevention programme at a sufficient scale. Recently, the 'HIV counselling & testing' (HCT) campaign is gaining public attention, where HIV patients are identified through screening and immediately sent under a course of antiretroviral treatment (ART), neglecting the time extent they have been infected. In this article, we study a nonlinear mathematical model for the transmission dynamics of HIV/AIDS system receiving drug treatment along with effective awareness programs through media. Here, we consider two different circumstances: when treatment is only effective and when both treatment and awareness are included. The model is analyzed qualitatively using the stability theory of differential equations. The global stabilities of the equilibria under certain conditions are determined in terms of the model reproduction number. The effects of changes in some key epidemiological parameters are investigated. Projections are made to predict the long term dynamics of the disease. The epidemiological implications of such projections on public health planning and management are discussed. These studies show that the aware populations were less vulnerable to HIV infection than the unaware population.

show abstract

“…This is due to the opposite time orientations of the optimality system; the state problem has initial values and the adjoint problem has final values. This restriction is very common in control problems (see [6,28,32,33]). Next we discuss the numerical solutions of the optimality system and the corresponding optimal control pair, the parameter choices, and the interpretations from various cases.…”

Section: Optimal Control Analysis Of the Leptospirosis Modelmentioning

confidence: 99%

Global stability analysis and control of leptospirosis

2016

Self Cite

View full text Add to dashboard Cite

Abstract:The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters' case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model's parameters are calculated. In the time-dependent constant control case, Pontryagin's Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.

show abstract

A Model for Control of Hiv/Aids With Parental Care

Cited by 12 publications

References 16 publications

Optimal control and sensitivity analysis of SIV→HIV dynamics with effects of infected immigrants in sub‐Saharan Africa

Optimal control and sensitivity analysis of SIV→HIV dynamics with effects of infected immigrants in sub‐Saharan Africa

A Comparative Study Between Two Systems with and Without Awareness in Controlling HIV/AIDS

Global stability analysis and control of leptospirosis

Contact Info

Product

Resources

About