# Going Back to Fundamentals: Three Marriageable Actions for Thalassemia and Carrier Population Management

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methods

- (i)
- Children population under the age of 20: normal children ${G}_{M}$/${G}_{F}$ and (thalassemia) carrier children ${G}_{C}^{M}$/${G}_{C}^{F};$
- (ii)
- Single adult population over the age of 20: normal adult singles ${S}_{M}$/${S}_{F}$ and carrier adult singles ${C}_{M}$/${C}_{F}$;
- (iii)
- Thalassemia major population: ${T}_{M}$/${T}_{F}$;
- (iv)
- Married population groups: normal-to-normal married group ${U}_{1},$ normal-to-carrier/ carrier-to-normal married group ${U}_{2},$ and carrier-to-carrier married group ${U}_{3},$

- A1.
- Thalassemia control measures are newborn baby screening and premarital screening.
- A2.
- The newborn baby screening is given to almost all newborn babies, and the premarital screening is provided to all about-to-marry couples.
- A3.
- People who receive a thalassemia control measure can reconsider their marriage decision.
- A4.
- Thalassemia major population group has a very low chance of marriage due to prolonged treatments. Hence, the marriage rate of the thalassemia major population groups is negligible.
- A5.
- Marriageable actions are actions of searching for spouses by marriageable adults who are above twenty years of age.
- A6.
- Since three marriageable actions such as normal-to-carrier, carrier-to-normal and carrier-to-carrier marriages can affect thalassemia and carrier populations, they will be in focus. A normal-to-carrier (carrier-to-normal) marriage means that a normal (carrier) individual chooses to marry a carrier (normal) individual. A carrier-to-carrier marriage implies that a carrier individual decides to marry a carrier individual.
- A7.
- Except for the thalassemia major population group, all other groups can marry with certain marriage rates.
- A8.
- The combinations of possible marriages among single males and females are
- •
- normal male × normal female
- •
- normal male × carrier female or carrier male × normal female
- •
- carrier male × carrier female

## 3. Results

#### 3.1. Impact of the Three Marriageable Actions

#### 3.2. Sensitivity Analysis of the Selected Model Parameters

## 4. Discussion

- 1.
- The eradication of thalassemia can be achieved by the 100% marriage reconsideration of carrier–carrier couples;
- 2.
- Promoting normal-to-carrier marriage will not achieve the eradication of thalassemia at all, but can help reduce the thalassemia population by a small point;
- 3.
- Encouraging carrier-to-normal marriage will make the eradication of thalassemia possible because of its indirect effect of reconsideration of carrier-to-carrier marriage (i.e., the more carrier-to-normal marriage the less carrier-to-carrier marriage);
- 4.
- Carrier-to-normal marriage may be more effective in reducing the carrier population than normal-to-carrier marriage.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Mathematical Model

- (v1)
- ${G}_{M}$ and ${G}_{F}$ are boys and girls (children);
- (v2)
- ${G}_{M}^{C}$ and ${G}_{F}^{C}$ are carrier boys and girls (children);
- (v3)
- ${T}_{M}$ and ${T}_{F}$ are the male and female thalassemia major population groups;
- (v4)
- ${S}_{M}$ and ${S}_{F}$ are the single male and female population groups;
- (v5)
- ${C}_{M}$ and ${C}_{F}$ are the single male and female carrier population groups;
- (v6)
- ${U}_{1}$ is the normal-to-normal married group;
- (v7)
- ${U}_{2}$ is the normal-to-carrier/carrier-to-normal married group;
- (v8)
- ${U}_{3}$ is the carrier-carrier married group.

- (p1)
- ${b}_{M}$ and ${b}_{F}$ are the birth rates of boys and girls, respectively;
- (p2)
- ${d}_{M}$ and ${d}_{F}$ are the natural death rates of male and female, and ${d}_{T}$ is the thalassemia induced death rate;
- (p3)
- ${\gamma}_{M}$ and ${\gamma}_{F}$ are the proportions of children becoming adults;
- (p4)
- ${\eta}_{CG}^{M}$ and ${\eta}_{CG}^{F}$ are the proportions of being identified as carrier babies from the newborn baby screening;
- (p5)
- ${\beta}_{S}^{M}$ and ${\beta}_{S}^{F}$ are the newborn baby screening rates for male and female, respectively;
- (p6)
- ${\alpha}_{S}^{M}$ and ${\alpha}_{S}^{F}$ are the premarital screening rates for male and female, respectively;
- (p7)
- ${\eta}_{T}^{M}$ and ${\eta}_{T}^{F}$ are the rates of being diagnosed as thalassemia major of male and female, respectively;
- (p8)
- ${\epsilon}_{1}$ is the proportion of normal population getting married with carrier population, i.e., the chance of normal-to-carrier marriage. Therefore, $(1-{\epsilon}_{1})$ is the proportion of normal population getting married with normal population;
- (p9)
- ${\epsilon}_{2}$ is the proportion of carrier population getting married with normal population, i.e., the chance of carrier-to-normal marriage. Therefore, $(1-{\epsilon}_{2})$ is the proportion of carrier population getting married with carrier population;
- (p10)
- $\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}{d}_{M}^{G}$ and ${d}_{F}^{G}$ are child mortality rates;
- (p11)
- $\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\nu $ is the marriage reconsideration rates of carrier-carrier couples.

- Normal children population groups (${G}_{M}$ and ${G}_{F}$)In Equations (A1) and (A2), ${b}_{M}$ and ${b}_{F}$ are birth of boys and girls, ${\zeta}_{1}{\eta}_{T}^{M}{\beta}_{S}^{M}{G}_{M}$ and ${\zeta}_{1}{\eta}_{T}^{F}{\beta}_{S}^{F}{G}_{F}$ are children diagnosed as the thalassemia population from the newborn baby screening. ${\zeta}_{2}{\eta}_{CG}^{M}{\beta}_{S}^{M}{G}_{M}$ and ${\zeta}_{2}{\eta}_{CG}^{F}{\beta}_{S}^{F}{G}_{F}$ are children diagnosed as thalassemia carrier population from the newborn baby screening. ${\gamma}_{M}{G}_{M}$ and ${\gamma}_{F}{G}_{F}$ are children who become adults. ${d}_{M}^{G}{G}_{M}$ and ${d}_{F}^{G}{G}_{F}$ are death of the children population.
- Carrier children population groups (${G}_{M}^{C}$ and ${G}_{F}^{C}$)In Equations (A3) and (A4), ${\zeta}_{2}{\eta}_{CG}^{M}{\beta}_{S}^{M}{G}_{M}$ and ${\zeta}_{2}{\eta}_{CG}^{F}{\beta}_{S}^{F}{G}_{F}$ are children diagnosed as thalassemia carrier population from the newborn newborn baby screening. ${\gamma}_{M}{G}_{M}^{C}$ and ${\gamma}_{F}{G}_{F}^{C}$ are carrier children who become young adults. ${d}_{M}^{G}{G}_{M}^{C}$ and ${d}_{F}^{G}{G}_{F}^{C}$ are death of the carrier children population.
- Thalassemia population groups (${T}_{M}$ and ${T}_{F}$)In Equations (A5) and (A6), ${\zeta}_{1}{\eta}_{T}^{M}{\beta}_{S}^{M}{G}_{M}$ and ${\zeta}_{1}{\eta}_{T}^{F}{\beta}_{S}^{F}{G}_{F}$ are children diagnosed as thalassemia population from the newborn newborn baby screening. ${d}_{T}{T}_{M}$ and ${d}_{T}{T}_{F}$ is the death of thalassemia population due to the illness.
- Normal single male and female population groups (${S}_{M}$ and ${S}_{F}$)In Equations (A7) and (A8), ${\gamma}_{M}{G}_{M}$ and ${\gamma}_{F}{G}_{F}$ are normal single adult males and females. ${\alpha}_{S}^{M}{S}_{M}$ and ${\alpha}_{S}^{F}{S}_{F}$ are populations who take the premarital screening when they are about to marry. ${d}_{M}{S}_{M}$ and ${d}_{M}{S}_{F}$ are death of normal male and female singles, respectively.
- Carrier single male and female population groups (${C}_{M}$ and ${C}_{F}$)In Equations (A9) and (A10), ${\gamma}_{M}{G}_{M}^{C}$ and ${\gamma}_{F}{G}_{F}^{C}$ are carrier single males and females who are young adults. ${\alpha}_{S}^{M}{C}_{M}$ and ${\alpha}_{S}^{F}{C}_{F}$ are carrier singles who take the premarital screening when they are about to marry. $\nu (1-{\epsilon}_{2}){\alpha}_{S}^{M}{C}_{M}$ and $\nu (1-{\epsilon}_{2}){\alpha}_{S}^{F}{C}_{F}$ are carrier singles resulted from the marriage reconsideration of carrier–carrier couples. ${d}_{M}{C}_{M}$ and ${d}_{M}{C}_{F}$ are death of the carrier singles, respectively.
- Normal-to-normal married population groups (${U}_{1}$)In Equation (A11), $(1-{\epsilon}_{1})({\alpha}_{S}^{M}{S}_{M}+{\alpha}_{S}^{F}{S}_{F})$ is the proportion of normal population getting married with normal population who went through the premarital screening. $\mu {U}_{1}$ is the death of this married group.
- Normal-to-carrier/carrier-to-normal married population group (${U}_{2}$)In Equation (A12), ${\epsilon}_{1}({\alpha}_{S}^{M}{S}_{M}+{\alpha}_{S}^{F}{S}_{F})$ is the proportion of normal population getting married with carrier population, and ${\epsilon}_{2}({\alpha}_{S}^{M}{C}_{M}+{\alpha}_{S}^{F}{C}_{F}))$ is the proportion of carrier population getting married with normal population. $\mu {U}_{2}$ is the death of this married group.
- Carrier-to-carrier married population group (${U}_{3}$)In Equation (A13), $(1-\nu )(1-{\epsilon}_{2})({\alpha}_{S}^{M}{C}_{M}+{\alpha}_{S}^{F}{C}_{F})$ is the carrier–carrier couples who proceed to marry regardless of their premarital screening result. $\mu {U}_{3}$ is the death of this married group.

#### Appendix A.2. Analysis of the Model

**Theorem**

**A1.**

**Proof.**

**Theorem**

**A2**

**Proof.**

- ${A}_{1}={E}_{1}+{C}_{1}+{C}_{3},$${A}_{11}=\frac{{G}_{M}}{U}({E}_{1}+{C}_{1}),$${A}_{12}=\frac{{G}_{M}}{U}({E}_{1}+{C}_{1}-{\eta}_{CG}^{M}{\beta}_{S}^{M}),$ and${A}_{13}=\frac{{G}_{M}}{U}({\eta}_{T}^{M}{\beta}_{S}^{M}+{\eta}_{CG}^{M}{\beta}_{S}^{M}-{E}_{1}-{C}_{1})$
- ${B}_{2}={F}_{2}+{D}_{2}+D4,$${B}_{11}=\frac{{G}_{F}}{U}({F}_{2}+{D}_{2}),$${B}_{12}=\frac{{G}_{F}}{U}({F}_{2}+{D}_{2}-{\eta}_{CG}^{F}{\beta}_{S}^{F})$ and${B}_{13}=\frac{{G}_{F}}{U}({\eta}_{T}^{F}{\beta}_{S}^{F}+{\eta}_{CG}^{F}{\beta}_{S}^{F}-{F}_{2}-{D}_{2})$
- ${E}_{1}={\zeta}_{1}{\eta}_{T}^{M}{\beta}_{S}^{M},$${C}_{1}={\zeta}_{2}{\eta}_{CG}^{M}{\beta}_{S}^{M},$ and ${C}_{3}={\gamma}_{M}+{d}_{M}^{G}$
- ${F}_{2}={\zeta}_{1}{\eta}_{T}^{F}{\beta}_{S}^{F},$${D}_{2}={\zeta}_{2}{\eta}_{CG}^{F}{\beta}_{S}^{F},$ and ${D}_{4}={\gamma}_{F}+{d}_{F}^{G}$
- $C}_{11}=\frac{{G}_{M}}{U}{C}_{1$ and ${C}_{12}=\frac{{G}_{M}}{U}({\eta}_{CG}^{M}{\beta}_{S}^{M}-{C}_{1})$
- $D}_{11}=\frac{{G}_{F}}{U}{D}_{2$ and ${D}_{12}=\frac{{G}_{F}}{U}(+{\eta}_{CG}^{F}{\beta}_{S}^{F}-{D}_{2})$
- $E}_{11}=\frac{{G}_{M}}{U}{E}_{1$ and ${E}_{13}=\frac{{G}_{M}}{U}({\eta}_{T}^{M}{\beta}_{S}^{M}-{E}_{1})$
- $F}_{11}=\frac{{G}_{F}}{U}{F}_{2$ and ${F}_{13}=\frac{{G}_{F}}{U}({\eta}_{T}^{F}{\beta}_{S}^{F}-{F}_{2})$
- ${G}_{7}={\alpha}_{S}^{M}+{d}_{M}$ and ${H}_{8}={\alpha}_{S}^{F}+{d}_{F}$
- ${I}_{9}={\alpha}_{S}^{M}-\nu (1-{\epsilon}_{2}){\alpha}_{S}^{M}+{d}_{M}$ and ${J}_{10}={\alpha}_{S}^{F}-\nu (1-{\epsilon}_{2}){\alpha}_{S}^{F}+{d}_{F}$
- ${K}_{7}=(1-{\epsilon}_{1}){\alpha}_{S}^{M}$ and ${K}_{8}=(1-{\epsilon}_{1}){\alpha}_{S}^{F}$
- ${M}_{9}=(1-\nu )(1-{\epsilon}_{2}){\alpha}_{S}^{M}$ and ${M}_{10}=(1-\nu )(1-{\epsilon}_{2}){\alpha}_{S}^{F}.$

- ${\tilde{C}}_{11}={C}_{11}-{A}_{11}\frac{{C}_{1}}{{A}_{1}},$${\tilde{C}}_{12}={C}_{12}+{A}_{12}\frac{{C}_{1}}{{A}_{1}},$ and $\tilde{C}}_{13}=-{C}_{12}+{A}_{13}\frac{{C}_{1}}{{A}_{1}$
- ${\tilde{D}}_{11}={D}_{11}-{B}_{11}\frac{{D}_{2}}{{B}_{2}},$$\tilde{D}}_{12}={D}_{12}+{B}_{12}\frac{{D}_{2}}{{B}_{2}$ and $\tilde{D}}_{13}=-{D}_{12}+{B}_{13}\frac{{D}_{2}}{{B}_{2}$
- ${\tilde{E}}_{11}={E}_{11}-{A}_{11}\frac{{E}_{1}}{{A}_{1}},$${\tilde{E}}_{12}={E}_{11}-{A}_{12}\frac{{E}_{1}}{{A}_{1}},$ and $\tilde{E}}_{13}=-{E}_{13}+{A}_{13}\frac{{E}_{1}}{{A}_{1}$
- ${\tilde{F}}_{11}={F}_{11}-{B}_{11}\frac{{F}_{2}}{{B}_{2}},$$\tilde{F}}_{12}={F}_{11}-{B}_{12}\frac{{F}_{2}}{{B}_{2}$ and $\tilde{F}}_{13}=-{F}_{13}+{B}_{13}\frac{{F}_{2}}{{B}_{2}$
- ${G}_{11}={A}_{11}\frac{{\gamma}_{M}}{{A}_{1}},$${G}_{12}={A}_{12}\frac{{\gamma}_{M}}{{A}_{1}},$ and $G}_{13}={A}_{13}\frac{{\gamma}_{M}}{{A}_{1}$
- ${H}_{11}={B}_{11}\frac{{\gamma}_{F}}{{B}_{2}},$${H}_{12}={B}_{12}\frac{{\gamma}_{F}}{{B}_{2}},$ and $H}_{13}={B}_{13}\frac{{\gamma}_{F}}{{B}_{2}$
- ${I}_{11}=-{C}_{11}\frac{{\gamma}_{M}}{{C}_{3}},$${I}_{12}={C}_{12}\frac{{\gamma}_{M}}{{C}_{3}},$ and $I}_{13}={C}_{12}\frac{{\gamma}_{M}}{{C}_{3}$
- ${J}_{11}=-{D}_{11}\frac{{\gamma}_{F}}{{D}_{4}},$${J}_{12}={D}_{12}\frac{{\gamma}_{F}}{{D}_{4}},$ and $J}_{13}={D}_{12}\frac{{\gamma}_{F}}{{D}_{2}$
- ${K}_{11}=\mu -\left({G}_{11}\frac{{K}_{7}}{{G}_{7}}+{H}_{12}\frac{{K}_{8}}{{H}_{8}}\right)$$\phantom{\rule{2.em}{0ex}}=\mu -\left(\frac{{G}_{M}({E}_{1}+{C}_{1}){\gamma}_{M}{K}_{7}}{U({E}_{1}+{C}_{1}+{C}_{3}){G}_{7}}+\frac{{G}_{F}({F}_{2}+{D}_{2}-{\eta}_{CG}^{F}{\beta}_{S}^{F}){\gamma}_{F}{K}_{8}}{U({F}_{2}+{D}_{2}+{D}_{4}){H}_{8}}\right)>0$$K}_{12}={G}_{12}\frac{{K}_{7}}{{J}_{7}}+{H}_{12}\frac{{K}_{8}}{{H}_{8}$ and $K}_{13}={G}_{13}\frac{{K}_{7}}{{J}_{7}}+{H}_{13}\frac{{K}_{8}}{{H}_{8}$
- $L}_{11}={J}_{11}\frac{{\epsilon}_{1}{\alpha}_{S}^{F}}{{J}_{10}}+{I}_{11}\frac{{\epsilon}_{1}{\alpha}_{S}^{M}}{{J}_{9}}+{H}_{11}\frac{{\epsilon}_{1}{\alpha}_{S}^{F}}{{H}_{8}}+{G}_{11}\frac{{\epsilon}_{1}{\alpha}_{S}^{F}}{{G}_{7}$${L}_{12}=\mu -\left({K}_{12}\frac{{L}_{11}}{{K}_{11}}+{J}_{12}\frac{{\epsilon}_{1}{\alpha}_{S}^{F}}{{J}_{10}}+{I}_{12}\frac{{\epsilon}_{1}{\alpha}_{S}^{M}}{{I}_{9}}+{H}_{12}\frac{{\epsilon}_{1}{\alpha}_{S}^{F}}{{H}_{8}}+{G}_{12}\frac{{\epsilon}_{1}{\alpha}_{S}^{M}}{{G}_{7}}\right)>0$$L}_{13}={J}_{13}\frac{{\epsilon}_{1}{\alpha}_{S}^{F}}{{J}_{10}}+{I}_{13}\frac{{\epsilon}_{1}{\alpha}_{S}^{M}}{{J}_{9}}+{H}_{13}\frac{{\epsilon}_{1}{\alpha}_{S}^{F}}{{H}_{8}}+{G}_{13}\frac{{\epsilon}_{1}{\alpha}_{S}^{F}}{{G}_{7}}+{K}_{13}\frac{{L}_{11}}{{K}_{11}$
- $M}_{11}={J}_{11}\frac{{M}_{10}}{{J}_{10}$ and $M}_{12}={K}_{12}\frac{{M}_{11}}{{K}_{11}}+{J}_{12}\frac{{M}_{9}}{{J}_{10}}+{I}_{12}\frac{{M}_{9}}{{I}_{9}$${M}_{13}=\mu -\left({K}_{13}\frac{{M}_{11}}{{K}_{11}}+{J}_{13}\frac{{M}_{10}}{{J}_{10}}+{I}_{13}\frac{{M}_{9}}{{I}_{9}}\right)>0.$

## References

- Thalassemia Foundation of Canada. Guidelines for the Clinical Care of Patients with Thalassemia in Canada. 2009. Available online: http://www.thalassemia.ca/resources/ (accessed on 15 July 2022).
- Cao, A.; Galanello, R. Beta-thalassemia. Genet. Med.
**2010**, 12, 61–76. [Google Scholar] [CrossRef] [PubMed] - Danjou, F.; Anni, F.; Galanello, R. Beta-thalassemia: From genotype to phenotype. Haematologica
**2011**, 96, 1573–1575. [Google Scholar] [CrossRef] [PubMed] - Weatherall, D. The inherited diseases of hemoglobin are an emerging global health burden. Blood
**2010**, 115, 4331–4336. [Google Scholar] [CrossRef] [PubMed] - Alwash, R.; Abbas, A. Beta-thalassemia. Public Health Med.
**1999**, 1, 61–76. [Google Scholar] - WHO. Genes and Human Disease. Available online: http://www.who.int/genomics/public/geneticdiseases/en/index2.html (accessed on 15 July 2022).
- Modell, B.; Darlison, M. Global epidemiology of haemoglobin disorders and derived service indicators. Bull. World Health Organ.
**2008**, 86, 480–487. [Google Scholar] [CrossRef] [PubMed] - Weatherall, D. Thalassemia as a global health problem: Recent progress toward its control in the developing countries. Ann. N. Y. Acad. Sci.
**2010**, 86, 480–487. [Google Scholar] [CrossRef] [PubMed] - Al-Gazali, L.; Alwash, R.; Abdulrazzaq, Y. United Arab Emirates: Communities and Community Genetics. Public Health Genom.
**2005**, 8, 186–196. [Google Scholar] [CrossRef] [PubMed] - Al-Gazali, L.; Alwash, R.; Abdulrazzaq, Y. Mutations of a country: A mutation review of single gene disorders in the United Arab Emirates (UAE). Hum. Mutat.
**2010**, 31, 505–520. [Google Scholar] [CrossRef] [PubMed] - Hamamy, H.; Antonarakis, S.; Cavalli-Sforza, L.; Temtamy, S.; Romeo, G.; Kate, L.; Bennett, R.L.; Shaw, A.; Megarbane, A.; van Duijn, C.; et al. Consanguineous marriages, pearls and perils: Geneva International Consanguinity Workshop Report. Genet. Med.
**2011**, 13, 841–847. [Google Scholar] [CrossRef] [PubMed] - Tadmouri, G.; Nair, P.; Obeid, T.; Ali, M.A.; Hamamy, N.A.K.H. Consanguinity and reproductive health among Arabs. Reprod. Health
**2009**, 6, 1–9. [Google Scholar] [CrossRef] [PubMed] - Denic, S.; Aden, B.; Nagelkerke, N.; Essa, A. β-Thalassemia in Abu Dhabi: Consanguinity and tribal stratification are major factors explaining the high prevalence of the disease. Hemoglobin
**2013**, 37, 351–358. [Google Scholar] [CrossRef] [PubMed] - Bittles, A. Reproductive behavior and health in consanguineous marriages. Science
**1991**, 252, 789–794. [Google Scholar] [CrossRef] [PubMed] - Bittles, A. The impact of consanguinity on neonatal and infant health. Early Hum. Dev.
**2010**, 86, 737–741. [Google Scholar] [CrossRef] [PubMed] - Baysal, E. Molecular Heterogeneity of Beta-Thalassemia in the United Arab Emirates. Community Genet.
**2005**, 8, 35–39. [Google Scholar] [CrossRef] [PubMed] - Baysal, E. Molecular Basis of β-Thalassemia in the United Arab Emirates. Hemoglobin
**2011**, 35, 581–588. [Google Scholar] [CrossRef] [PubMed] - Al-Dabbagh, B.; Shawqi, S.; Yasin, J.; Al Essa, A.; Nagelkerke, N.; Denic, S. Half of the Emirati Population Has Abnormal Red Cell Parameters: Challenges for Standards and Screening Guidelines. Hemoglobin
**2013**, 38, 56–59. [Google Scholar] [CrossRef] [PubMed] - Health Authority Abu Dhabi. Health Statistics 2013. Available online: https://scad.gov.ae/Release%20Documents/health%202013.pdf (accessed on 15 July 2022).
- Belhoul, K.; Abdulrahman, M.; Alraei, R. Hemoglobinopathy carrier prevalence in the United Arab Emirates: First analysis of the Dubai health authority premarital screening program results. Hemoglobin
**2013**, 37, 359–368. [Google Scholar] [CrossRef] [PubMed] - Sheikh Saud bin Saqr Al Qasimi Foundation for Policy Research. Public Health in the United Arab Emirates and Ras Al Khaimah. 2015. Available online: https://publications.alqasimifoundation.com/en/public-health-in-the-united-arab-emirates-and-ras-al-khaimah-2021 (accessed on 15 July 2022).
- Federal Competitiveness and Statistics Authority. Statistics by Subjects. 2015. Available online: https://fcsc.gov.ae/en-us/Pages/Statistics/Statistics-by-Subject.aspx#/%3Ffolder=Economy/National%20Account/National%20Account (accessed on 15 July 2022).
- Statistics Center Abu Dhabi. Statistical Yearbook of Abu Dhabi. 2013. Available online: https://www.scad.ae/Release%20Documents/SYB%202013%20English%20-full%20version.pdf (accessed on 15 July 2022).
- R Development Core Team. R: A Language and Environment for Statistical Computing; R Development Core Team: Vienna, Austria, 2016. [Google Scholar]
- Soetaert, K.; Petzoldt, T. Inverse modeling, sensitivity and Monte Carlo analysis in R using package FME. J. Stat. Softw.
**2010**, 33, 1–28. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Numerical simulations of thalassemia and carrier population with the initial data ${G}_{M}={G}_{M}^{C}$ = 16,040, ${G}_{F}={G}_{F}^{C}$ = 15,350, ${T}_{M}=120,$ ${T}_{F}=100,$ ${S}_{M}$ = 100,000, ${S}_{F}=100,000,$ ${C}_{M}$ = 85,000, ${C}_{F}$ = 90,000, ${U}_{1}$ = 15,000, ${U}_{2}$ = 30,000, and ${U}_{3}=5000$ and parameter values in Table 1. The value 0.2 means 20% rate and 1 100% rate in the legend. (

**A**) Under various marriage reconsideration rates ($\nu $). (

**B**) Under various chances (${\epsilon}_{1}$) of normal-to-carrier marriage. (

**C**) Under various chances (${\epsilon}_{2}$) of carrier-to-normal marriage.

**Figure 3.**Numerical simulations of three married groups ${U}_{1},$ ${U}_{2},$ and ${U}_{3}$ with the initial data ${G}_{M}={G}_{M}^{C}=16,040,$${G}_{F}={G}_{F}^{C}$ = 15,350, ${T}_{M}=120,$ ${T}_{F}=100,$ ${S}_{M}$ = 100,000, ${S}_{F}$ = 100,000, ${C}_{M}$ = 85,000, ${C}_{F}$ = 90,000, ${U}_{1}$ = 15,000, ${U}_{2}$ = 30,000, and ${U}_{3}=5000$ and parameter values in Table 1. The value 0.2 means 20% rate and 1 100% rate in the legend. (

**A**) Under various marriage reconsideration rates ($\nu $). (

**B**) Under various chances (${\epsilon}_{1}$) of normal-to-carrier marriage. (

**C**) Under various chances (${\epsilon}_{2}$) of carrier-to-normal marriage.

**Figure 4.**Sensitivity of significant parameters on thalassemia and carrier population (${T}_{M}$ and ${C}_{M}$). (

**A**) Sensitivity of ${\epsilon}_{1},$ $\nu ,$ ${\eta}_{CG}^{M},$ ${\eta}_{T}^{M}$ and ${\epsilon}_{2}$ on thalassemia population (${T}_{M}$) (the little box is the enlarged plot of ${\epsilon}_{1},$ $\nu ,$ ${\eta}_{CG}^{M},$ for eyes). (

**B**) Sensitivity of ${\epsilon}_{2},$ ${\epsilon}_{1},$ ${\eta}_{CG}^{M},$ ${\eta}_{T}^{M}$ and ${\alpha}_{M}^{S}$ on carrier population (${C}_{M}$). See parameter names shown in Table 1.

**Figure 5.**Sensitivity of significant parameters on three married groups, normal-normal marriages (${U}_{1}$), normal-carrier marriages (${U}_{2}$), and carrier-carrier marriages (${U}_{3}$). (

**A**) Sensitivity of ${\eta}_{CG}^{M},$ ${\eta}_{CG}^{F},$ ${\alpha}_{M}^{S},$ and ${\epsilon}_{1}$ on ${U}_{1}.$ (

**B**) Sensitivity of ${\eta}_{CG}^{M},$ ${\eta}_{CG}^{F},$ ${\alpha}_{F}^{S},$ ${\alpha}_{M}^{S},$ ${\epsilon}_{1},$ and ${\epsilon}_{2}$ on ${U}_{2}.$ (

**C**) Sensitivity of ${\eta}_{CG}^{M},$ $\nu ,$ ${\eta}_{CG}^{F},$ ${\alpha}_{M}^{S},$ ${\alpha}_{F}^{S}$ and ${\epsilon}_{2}$ on ${U}_{3}$ (the little box is the enlarged plot of ${\eta}_{CG}^{M},$ $\nu ,$ ${\eta}_{CG}^{F},$ ${\alpha}_{M}^{S},$ ${\alpha}_{F}^{S}$ for eyes). See parameter names shown in Table 1.

Parameter | Male | Female | Ref. |
---|---|---|---|

Birth rates | ${b}_{M}=8716$ | ${b}_{F}=7954$ | [22] |

Child mortality rates ${}^{\u2020}$ | ${d}_{M}^{G}=0.014$ | ${d}_{F}^{G}=0.008$ | [23] |

Adult death rates ${}^{\u2020}$ | ${d}_{M}=0.003$ | ${d}_{F}={\mu}^{\u2020\u2020}=0.0019$ | [22] |

Thalassemia induced death rate ${}^{\u2020}$ | ${d}_{T}=0.016$ | ${d}_{T}=0.016$ | [1] |

Proportion of young adults ${}^{\u2020}$ | ${\gamma}_{M}=0.0433$ | ${\gamma}_{F}=0.0447$ | [19] |

Newborn baby screening rate | ${\beta}_{S}^{M}={\beta}_{S}^{F}=1$ | [6] | |

Thalassemia detection adjusting rates | ${\eta}_{T}^{M}=0.0083$ | ${\eta}_{T}^{F}=0.0075$ | [6] |

Thalassemia carrier | |||

detection adjusting rates | ${\eta}_{CG}^{M}=0.0416$ | ${\eta}_{CG}^{F}=0.05416$ | [17] |

Premarital screening rates ${}^{\u2020}$ | ${\alpha}_{S}^{M}=0.0227$ | ${\alpha}_{S}^{F}=0.0223$ | [22] |

Chance of normal population | |||

getting married with carrier population | ${\epsilon}_{1}=0.5$ * | − | |

Chance of carrier population | |||

getting married with normal population | ${\epsilon}_{2}=0.5$ * | − | |

Marriage reconsideration rate | |||

of carrier-carrier couples | $\nu =0.3$ * | − |

^{†}The unit of the parameter values is per person.

^{††}$\mu $ represents the proportion of married population who died during their marriage. * These parameter values are initially assigned to our computer simulations and will be varied for further investigations of their impacts.

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**MDPI and ACS Style**

Kim, S.; AlDhaheri, H.; Kim, S.-Y.
Going Back to Fundamentals: Three Marriageable Actions for Thalassemia and Carrier Population Management. *Thalass. Rep.* **2022**, *12*, 105-122.
https://doi.org/10.3390/thalassrep12030016

**AMA Style**

Kim S, AlDhaheri H, Kim S-Y.
Going Back to Fundamentals: Three Marriageable Actions for Thalassemia and Carrier Population Management. *Thalassemia Reports*. 2022; 12(3):105-122.
https://doi.org/10.3390/thalassrep12030016

**Chicago/Turabian Style**

Kim, Sehjeong, Hamda AlDhaheri, and So-Yeun Kim.
2022. "Going Back to Fundamentals: Three Marriageable Actions for Thalassemia and Carrier Population Management" *Thalassemia Reports* 12, no. 3: 105-122.
https://doi.org/10.3390/thalassrep12030016