Mathematical models of HIV dynamics, disease development and treatment Essay

Wodarz and Nowak (2002) postulate that the dynamics between virus infections and the immune system involve many different components and are multi-factorials. The research paper reviewed on mathematical models of HIV dynamics, disease development and treatment. It starts by introducing a basic model of virus infection and show how it was used to investigate HIV dynamics and to measure critical parameters that contribute to a new understanding of the illness process. Besides discuss the diversity threshold model as an example of the common principle that virus development can drive disease movement and the devastation of the immune system. Finally, show how mathematical models can be used to understand relates of long term immunological control of HIV, and to plan therapy rules that change a developing patient into a state of long term non progression.
Duffin and Tullis (2002) found that for most people, infection with HIV is the shock of a progressive illness that effects in death due to the growing incidence of opportunistic contaminations. Mathematical models of HIV infection are vital to our considerate of AIDS. Nevertheless, most models do not forecast both the reduction in CD4+ T cells and the growth in viral load realized over the progression of infection. By including terms for constant loss of CD4+T cells and including change in viral permission and viral invention, two new models have been formed that correctly predict the dynamics of the illness. The first model is a clearance rate decrease model and is based on a 10% per year reduction in both viral clearance and CD4+T cell levels. A macrophage reservoir model include the remark that macrophage viral production rises up to 1000 folds in the existence of opportunistic infections that develop progressively common as disease growths. Both viral clearance and macrophage reservoir models predict the expected decline in T cell stages and rise in viral load detected at the beginning of AIDS.
Infections can be transferred many ways, some of which can be categorized as either horizontal or vertical. In the circumstance of HIV/AIDS, horizontal transmission can result from through physical contact between an infected individual and a vulnerable individual (Waziri, Massawe & Makinde, 2012). This research studies the dynamics of HIV/AIDS with treatment and vertical transmission. A nonlinear deterministic mathematical model for the problem is planned and investigated qualitatively using the constancy theory of differential equations. Local stability of the illness free equilibrium of the model was recognized by the next generation method. The outcomes display that the disease free equilibrium is closed by stable at beginning parameter less than unity and unstable at beginning parameter greater than unity. Universally, the disease free equilibrium is not stable due presence of forward division at beginning parameter equal to unity. Though, it is revealed that using treatment measures and control of the rate of vertical transmission has the influence of reducing the transmission of the disease considerably. Numerical simulation of the model is applied to examine the understanding of certain key parameters on the extent of the disease.