代写Research Project for STEM代写Matlab语言

2025-05-20 代写Research Project for STEM代写Matlab语言

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Research Project for STEM

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Project Report and Artefact

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Sickle Cell Trait in Ghana: Balancing Malaria Resistance and Sickle Cell Mortality

1. Introduction

1.1Aims and Objective

Sickle cell disease is an inherited blood disorder caused by mutations in the hemoglobin gene. Patients' red blood cells twist from their normal disk shape into a sickle shape when starved of oxygen(Rees et al., 2010), which can lead to blocked blood vessels, tissue hypoxia and chronic inflammation, eventually leading to multiple organ damage.(Piel et al., 2017). As shown in Figure 1(Sundd P el al ,.2019).

Figure1 Schematic diagram of some pathophysiological processes in sickle cell anemia (Inusa, B.P.D., el al ,.2019).

Malaria is a parasitic disease caused by infection with Plasmodium and transmitted through the bite of the female Anopheles mosquito. Globally, approximately 240 million people are infected each year and 600,000 die, 95% of which occur in Africa (WHO, 2022). As shown in Figure 2 below .

Figure 2 Life Cycle of P. falciparum (Cowman, A. F., el al ,.2016)

Furthermore,the research finding shows that there are some relationship of Malaria and Sickel cells disease. The sickle cell trait (AS) provides partial resistance to Plasmodium falciparum malaria(Williams et al., 2005), explaining its high prevalence in malaria-endemic regions.

So, This report will use MATLAB to simulate the mortality rate of sickle cell patients affected by Malaria in Ghana, analyze the trend of malaria transmission before and after policy intervention, and compare the effect of policy on malaria outbreak control.Assess whether the results of policy measures have an impact on mortality, and then combine projections with actual data to find effective methods.

1.2 Background study of Malaria and Sickle cells disease in Ghana

Ghana faces a dual burden of Malaria and Sickle cell disease (SCD). The evidence shows that Ghana has one of the highest malaria prevalence areas in sub-Saharan Africa , with more than 5 million malaria cases reported annually, accounting for 38% of outpatient cases (Ghana Health Service, 2023). Meanwhile, 2 % of all births in Ghana have sickle cell disease, and 27.2 % have sickle cell trait (AS), reflecting a historically balanced selection (Ghana Health Service, 2023). This proves that the AS genotype is partially resistant to severe malaria, because sickle cells have the ability to inhibit parasite proliferation, and this phenomenon allows the HbS gene to survive in malaria-endemic areas (Williams et al., 2005; Ansah et al., 2020). As shown in Figure 3.

Figure.3 Ghana distribution of the sickle cell gene(WHO,.2022)

Interactions between Malaria and Sickle cells are evident in regional differences in Ghana. Those research show that the prevalence of malaria among children in northern Ghana is 45%, which does attest to the kinship and healthcare disparities that contribute to the lower incidence of AS (24%) and higher incidence of SCD (3.5%), whereas southern urban areas such AS Accra have lower rates of malaria transmission (22%) but higher incidence of AS (32%) (Ansah et al., 2020; Penman et al., 2017) . At the same time, this paradox just highlights the advantages of heterozygotes (AS) : Heterozygotes with the sickle cell anemia gene (type AS) had a 70% lower risk of malaria death, which did offset the high mortality rate of up to 35% in newborns with untreated sickle cell anemia (SCD) by the age of five, thus stabilizing the frequency of the sickle hemoglobin (HbS) allele.(Owiredu et al., 2021).

Public health efforts also face conflicting priorities. Malaria interventions, such as insecticide-treated bed nets (60% coverage) and the R21 vaccine (75% effectiveness), have the potential to reduce the selective advantage of sickle cell anaemia (AS), thereby increasing the incidence of sickle cell disease (SCD) in the long term. Meanwhile, sickle cell disease programs - including newborn screening (coverage is 60%) and hydroxyurea therapy - continue to be hampered by resource shortages and stigma in rural areas (McGann et al., 2020). These integrated strategies, such as simultaneous screening for malaria and sickle cell anaemia in antenatal clinics, should be addressed to mitigate the possible unintended consequences of disease-specific policies (Ghana Health Services, 2023).

1.3 Research scope and limitation

This study focused on newborn deaths due to malaria and sickle cell disease (SCD) in Ghana. Nationally, 2 % of newborns inherit sickle cell disease (SS/SC genotype), and in untreated cases the mortality rate is 25 to 35 per cent due to sepsis and vascular obstruction before age 1 (Ansa et al., 2020; Narh et al., (2021)). Meanwhile, neonatal malaria, while less common than in older children, causes 12% of infant deaths in areas with high transmission, mainly due to placental transmission and delayed diagnosis (Ghana Health Services, 2023). The scope of the study included analysis of the overlap between sickle cell disease and malaria deaths, particularly in northern Ghana, where 40% of neonatal sickle cell disease deaths were associated with a positive malaria test result (Gyan et al., 2025). To assess the potential of interventions such as neonatal screening for sickle cell disease (coverage 60 %) to reduce double mortality.

Major limitations include under-reporting of malaria in newborns, as symptoms can often resemble septicaemia, which can lead to misclassification. Differences between urban and rural areas in access to diagnosis distort mortality estimates, while cultural differences limit the number of citizens who are reluctant to seek hospital delivery, which does mask the true mortality rate. Longitudinal data gaps hinder causal links between interventions (such as the R21 maternal vaccination trial) and mortality trends. Despite these limitations, the study highlights feasible strategies to reduce the double burden of disease in newborns in Ghana.

2. Methods

2.1 Model methods

The genetic patterns and evolutionary dynamics of sickle cell traits under malaria selection pressure have been extensively explored through mathematical models and empirical studies. The basic framework of cross-generation genotype frequency prediction is rooted in Mendelian inheritance principles(Hartl & Clark, 2007). Genetic transfer matrix is Let the genotype of the paternal parent be P{AA,AS,SS}The maternal genotype is G{AA,AS,SS} , The genotype of the offspring is C{AA,AS,SS}, Define three transfer matrices AA,AS,SS belongs to Rank Row 3×3 , element of matrix are which represents the probability that the offspring is genotype i when the parent is genotype j when the parent is genotype J.

Then, each matrix is multiplied by its corresponding individual frequency, and the resulting vector is multiplied by the initial frequency element by element, and finally the three results are summed to get the final value. As show in Table(1-3) below.

AA

parental/offspring

AA

AS

SS

AA

1

1/2

0

AS

0

1/2

1

SS

0

0

0

Table 1 AA offspring matrix

AS

parental/offspring

AA

AS

SS

AA

1/2

1/4

0

AS

1/2

1/2

1/2

SS

0

1/4

1/2

Table 2 AS offspring matrix

SS

parental/offspring

AA

AS

SS

AA

0

0

0

AS

1

1/2

0

SS

0

1/2

1

Table 3 SS offspring matrix

2.2 The basic model of sickle cells and malaria survivor

Based on the research of Hartl and Clark(2007), the figure 4 shows that the genetic matrix for a specific genotype iis used to calculate the progeny distribution(Hartl and Clark, 2007), the total progeny frequency P is the sum of individual progeny frequencies,The initial genotype frequencies are set to G=[0.708,0.272,0.02], which means the G(1)=0.708, G(2)=0.248, G(2)=0.02,G is the genotype frequency carrier, tracking AA, AS, SS genotypes in populations. It is central to the model because it is used to calculate progeny distribution, apply natural selection, and simulate the evolution of genotype frequencies across generations(Hartl and Clark,. 2007). :

Finally, the frequencies are standardized to ensure that their sum is 1.

Figure 4 The model of Sickle cell and Malaria Simulate without mortality

2.2 Dynamics of Sickle Cell Genotype Frequencies Under Selection Pressure

According to the research of Penman et al (2020). The figure 5 shows the model follows the evolution of genotype frequencies (AA, AS, SS) in a population of patients with sickle cell anemia. Natural selection is achieved by mortality rate SS= 0.073 (Makani et al. 2018):

The SS matrix is , then it get:

AA and AS remain unchanged: there is no selection pressure and the frequency is only fine-tuned for standardization.

Figure 5 The model of Sickle cell and Malaria Simulate with Sickle cell mortality

2.3 Analysis of Sickle Cell Genotype Frequency Dynamics with Malaria Selection Pressure

Based on the research, it claims that the proportion of mortality AA is 0.21Oxford Tropical Medicine 2023. The figure 6 shows the model follows the evolution of genotype frequencies (AA, AS, SS) in a population of patients with Malaria. Natural selection works by influencing mortality. The model demonstrates balanced polymorphism through differential survival (Hartl & Clark 2007) The application of natural selection pressure is achieved through matrix multiplication :

Then:

For loop:

1. Calculate the contribution of each genotype to the offspring (AA ,AS ,SS ).

2. The frequency of the merged offspring (Proportion of total) =(Proportion of AA+Proportion of AS+Proportion of SS).

3. Applying selective pressure (adjusting the frequency of SS).

4. Normalization of frequency(G=P/sum(P)).

5. Record the current frequency of AA,AS,SS.

Figure 6 The model of Sickle cell and Malaria Simulate with Malaria mortality

2.5 Dynamic evolution of genotype frequency under natural selection: a case study of selection pressure in sickle cell anemia and malaria

In this study, the figure 7 shows a matrix model was used to analyze the evolutionary dynamics of genotype frequencies (AA, AS, SS) under double selection pressures for malaria (affecting AA genotype) and sickle cell anemia (affecting SS genotype) (Penman et al,. 2020). The initial frequency was set at G= [0.708, 0.272, 0.02] , with a mortality rate of 21% for AA (malaria) and 7.3%(Makani et al. 2018) for SS (sickle cell anemia) (Oxford Tropical Medicine 2023). The propagation matrix AA, AS, S S encodes Mendelian inheritance laws for all possible parental pairings.:

Then:

Figure 7 The model of Sickle cell and Malaria Simulate with Malaria mortality and Sickle cell mortality

2.6 Mathematical analysis of a genetic transmission model of sickle cell malaria under the influence of mosquito nets

The figure 8 shows the MATLAB code is designed to simulate the evolution of sickle cell genotype frequencies (AA, AS, SS) under malaria selection pressure, incorporating the protective effects of insecticide-treated bed nets. The initial frequency was = [0.708; 0.272; 0.02] (Fikadu and Ashenafi, 2023). The model adjusts for malaria mortality based on bed net use 50% coverage, 18.8% effectiveness(Fikadu and Ashenafi, 2023), reducing the effective mortality rate for the AA genotype to:

The effective of bed net is:

Then:

Figure 8 The model of Sickle cell and Malaria Simulate with Malaria mortality under the bed net factor and sickle cell mortality

2.7 Mathematical analysis of a genetic transmission model of sickle cell malaria under the influence of mosquito nets and vaccine

This figure 9 shows that the MATLAB model adjusts for AA genotype mortality in combination with bed nets (75% coverage, 18.8% effectiveness) and malaria vaccines (13% effectiveness) :

Then:

Figure 9 The model of Sickle cell and Malaria Simulate with Malaria mortality under the bed net and Vaccine factor and sickle cell mortality