Abdessamad Tridane

Thalassemia in the United Arab Emirates: Why it can be prevented but not eradicated

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.

Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection

The aim of this paper is to study the early stage of HBV infection and impact delay in the infection process on the adaptive immune response, which includes cytotoxic T-lymphocytes and antibodies. In this stage, the growth of the healthy hepatocyte cells is logistic while the growth of the infected ones is linear. To investigate the role of the treatment at this stage, we also consider two types of treatment: interferon- (IFN) and nucleoside analogues (NAs). To find the best strategy to use this treatment, an optimal control approach is developed to find the possibility of having a functional cure to HBV.

Mathematical Analysis of a Delayed Hematopoietic Stem Cell Model with Wazewska–Lasota Functional Production Type

In this chapter, we consider a more general model describing the dynamics of a hematopoietic stem cell (HSC) model with Wazewska–Lasota functional production type describing the cycle of proliferating and quiescent phases. The model is governed by a system of two ordinary differential equations with discrete delay. Its dynamics are studied in terms of local stability and Hopf bifurcation. We prove the existence of the possible steady state and their stability with respect to the time delay and the apoptosis rate of proliferating cells. We show that a sequence of Hopf bifurcations occurs at the positive steady state as the delay crosses some critical values. We illustrate our results with some numerical simulations.

Population dynamics of Rift Valley fever, sleeping sickness, and vector-borne diseases brought by human migrations

Sleeping sickness (African trypanosomiasis), Rift Valley fever, and vectorborne diseases accompanying human migration have grown dramatically in recent years. That is why we propose this special issue, hoping to add to the understanding of population dynamics to prophylaxis. Climatic change modifies the geography of arboviruses. Moore et al. (2011) predicted that between 46 and 77 million people in Africa are at risk of catching sleeping sickness by 2090 due to climate change. Anyamba et al. (2002), Gagnon et al. (2002), and Sutherst (2004) associated outbreaks of Rift Valley fever and malaria with the El Niño southern oscillation. In this issue, Miron, Giordano, Kealey, and Smith? question the possible arrival of the Rift Valley fever in North America. They consider the interactions of humans, domestic livestock, and Aedes mosquitoes to show that the presence of this disease would lead to outbreaks every summer. They conclude that controlling the infection by spraying insecticide should be the most effective prophylaxis. No vaccine exists for the Rift Valley fever and for sleeping sickness in humans, but a recent vaccine for animals is promising (Bird et al., 2011). Samia, Kealey, and Smith? in this issue show that vaccination has limited efficacy, eventually failing to eradicate this disease. The rapid proliferation of the virus makes screening inane. More efficient prophylaxis should be the control of the tsetse fly and the infected livestock. However, if pesticide has been a handy measure against vector-borne diseases, it has favored resistant strains and is toxic to livestocks (Sutherst, 2004; Rivero et al., 2010). Human migration not only changes the geography of diseases but also modifies the dynamic of vector-born diseases (Stoddard et al., 2009). Sturrock et al. (2013), among others, suggested community screening to reduce the effect of human migration in the spreading of the disease. Kim, Tridane, and Chang in this issue show that, during an outbreak, border screening will not be effective if the lower bound of the basic reproduction number is greater than one. Rather, they advise a treatment at the local level of villages.

Human migrations and mosquito-borne diseases in Africa

ABSTRACT The efficacy of border screening as a prophylactic measure against mosquito-borne diseases in Africa depends on the value of the lower bound of the basic reproduction number. If this lower bound is greater than one, then border screening may be ineffective. In this case, the best prophylaxis is to isolate and treat patients in their region of residence.

Optimal Drug Treatment in a Simple Pandemic Switched System Using Polynomial Approach

The aim of this work is to investigate the optimal control of the treatment in a simple pandemic model as a switched nonlinear system. We used a newly developed approach based on the theory of moments. This approach allows to transform a nonlinear, non-convex optimal control problem to an equivalent linear and convex one. To illustrate our finding, we used the example of influenza pandemic to compare the full treatment approach to our optimal moment and time switching solution.