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Optimal control and sensitivity analysis of S I V → H I V dynamics with effects of infected immigrants in sub‐Saharan Africa
Author(s) -
Sule Amiru,
Abdullah Farah Aini
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4781
Subject(s) - basic reproduction number , mathematics , culling , sensitivity (control systems) , stability theory , immigration , transmission (telecommunications) , human immunodeficiency virus (hiv) , invariant (physics) , nonlinear system , demography , population , computer science , virology , biology , geography , sociology , herd , telecommunications , engineering , physics , ecology , quantum mechanics , electronic engineering , archaeology , mathematical physics
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 ℜ 0 <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 H I V disease spread.