Thalassemia is a genetic blood disorder that causes abnormal hemoglobin. Hemoglobin is a protein in red blood cells that carries oxygen and is made of two proteins from four α-globin genes and two β-globin genes. A defect in one or more of these genes causes thalassemia. The treatment of thalassemia mostly depends on life-long blood transfusions and removal of excessive iron from the blood stream. Such tremendous blood consumption puts pressure on the national blood stock in many countries. In particular, in the United Arab Emirates (UAE), various forms of thalassemia prevention have been used and hence, the substantial reduction of the thalassemia major population has been achieved. However, the thalassemia carrier population still remains high, which leads to the potential increase in the thalassemia major population through carrier-carrier marriages. In this work, we investigate the long-term impact and efficacy of thalassemia prevention measures via mathematical modeling at a population level. To our best knowledge, this type of assessment has not been done before and there is no mathematical model that has investigated such a problem for thalassemia or any blood disorders at a population level. By using UAE data, we perform numerical simulations of our model and conduct sensitivity analysis of parameter values to see which parameter values affect most the dynamics of our model. We discover that the prevention measures can contribute to reduce the prevalence of the disease only in the short term but not eradicate the disease in the long term.

We consider a switching system with time delay composed of a finite number of linear delay differential equations (DDEs). Each DDE consists of a sum of a linear ODE part and a linear DDE part. We study two particular cases: (a) all the ODE parts are stable and (b) all the ODE parts are unstable and determine conditions for delay independent stability. For case (a), we extend a standard result of linear DDEs via the multiple Lyapunov function and functional methods. For case (b) the standard DDE result is not directly applicable, however, we are able to obtain uniform asymptotic stability using the single Lyapunov function and functional methods.

Control strategies for gene regulatory networks have begun to be explored, both experimentally and theoretically, with implications for control of disease as well as for synthetic biology. Recent work has focussed on controls designed to achieve desired stationary states. Another useful objective, however, is the initiation of sustained oscillations in systems where oscillations are normally damped, or even not present. Alternatively, it may be desired to suppress (by damping) oscillations that naturally occur in an uncontrolled network. Here we address these questions in the context of piecewise-affine models of gene regulatory networks with affine controls that match the qualitative nature of the model. In the case of two genes with a single relevant protein concentration threshold per gene, we find that control of production terms (constant control) is effective in generating or suppressing sustained oscillations, while control of decay terms (linear control) is not effective. We derive an easily calculated condition to determine an effective constant control. As an example, we apply our analysis to a model of the carbon response network in Escherichia coli, reduced to the two genes that are essential in understanding its behavior.

We consider a switching system composed of a finite number of linear delay differential equations (DDE). It has been shown that the stability of a switching system composed of a finite number of linear ordinary differential equations (ODE) may be achieved by using a Common Lyapunov Function Method switching rule. We modify this switching rule for ODE systems to a Common Lyapunov Functional Method switching rule for DDE systems and show that it stabilizes our model. Our result uses a Riccati type Lyapunov functional under a condition on the time delay.

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