PRESENTING A MATHEMATICAL MODEL AND INVESTIGATING EFFECTS OF CONTAMINATED NEEDLE SHARING ON PREVALENCE OF HIV/AIDS DISEASE

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BABAEI AFSHIN; JAFARI HOSSEIN; AHMADI MASOUMEH

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Journal: ADVANCES IN MATHEMATICAL MODELING Year:2016 | Volume:5 | Issue:2 Page(s): 91-108

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Title

PRESENTING A MATHEMATICAL MODEL AND INVESTIGATING EFFECTS OF CONTAMINATED NEEDLE SHARING ON PREVALENCE OF HIV/AIDS DISEASE

Author(s)

BABAEI AFSHIN | JAFARI HOSSEIN | AHMADI MASOUMEH | Issue Writer Certificate

Keywords

HIVQ2

AIDS DISEASEQ2

MATHEMATICAL MODELQ1

REPRODUCTION NUMBERQ2

OPTIMAL CONTROLQ2

NEXT GENERATION MATRIXQ2

Abstract

In this paper, a MATHEMATICAL MODEL for studying HIV/AIDS dynamics is presented. Based on this model, the effects of contaminated needle sharing in addicted population on spread of HIV/AIDS is investigated. For this purpose, first, the effective REPRODUCTION NUMBER is obtained by using the next generation operator method. Then, the REPRODUCTION NUMBER is examined in two cases, one with sharing needles and the other one with not sharing needles. The OPTIMAL CONTROL problem is formulated by applying some controls on the disease model including use of non-shared and sterile needles, use of prevention methods, screening of unaware infectives and treating patients. Necessary conditions for OPTIMAL CONTROL is determined by using Pontryagin’s minimum principle. Finally, numerical results is obtained by the Runge–Kutta fourth-order method. The results show a significant difference in control of prevalence of disease between the cases applying and not applying control on the disease.

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APA: Copy

BABAEI, AFSHIN, JAFARI, HOSSEIN, & AHMADI, MASOUMEH. (2016). PRESENTING A MATHEMATICAL MODEL AND INVESTIGATING EFFECTS OF CONTAMINATED NEEDLE SHARING ON PREVALENCE OF HIV/AIDS DISEASE. ADVANCES IN MATHEMATICAL MODELING, 5(2), 91-108. SID. https://sid.ir/paper/243924/en

Vancouver: Copy

BABAEI AFSHIN, JAFARI HOSSEIN, AHMADI MASOUMEH. PRESENTING A MATHEMATICAL MODEL AND INVESTIGATING EFFECTS OF CONTAMINATED NEEDLE SHARING ON PREVALENCE OF HIV/AIDS DISEASE. ADVANCES IN MATHEMATICAL MODELING[Internet]. 2016;5(2):91-108. Available from: https://sid.ir/paper/243924/en

IEEE: Copy

AFSHIN BABAEI, HOSSEIN JAFARI, and MASOUMEH AHMADI, “PRESENTING A MATHEMATICAL MODEL AND INVESTIGATING EFFECTS OF CONTAMINATED NEEDLE SHARING ON PREVALENCE OF HIV/AIDS DISEASE,” ADVANCES IN MATHEMATICAL MODELING, vol. 5, no. 2, pp. 91–108, 2016, [Online]. Available: https://sid.ir/paper/243924/en

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