Incorporating social determinants of health into the mathematical modeling of HIV/AIDS

The theoretical mathematical design with the Social Determinants of Health has actually been established in phases.

Social determinants of health

For the choice of SDH that were included into the design, a narrative literature evaluation was carried out concentrated on peer-reviewed short articles, in PubMed/Medline and Scopus databases in between 2010 and 2020. This evaluation consisted of keywords HIV, AIDS and Social Determinants. An overall of 31 SDH were acquired in the evaluation, divided into 4 groups: Private Elements, Socioeconomic Elements, Social Involvement and Health Providers (Fig. 1). In the end, 4 determinants were chosen for incorporation into the design: Education, Work, Usage of Alcohol and drugs abuse and Condoms Usage. The option of these SDH was based upon the reoccurrence; acknowledged significance in the literature and the capability for measurement and metrology, in order to be included into the formulas of the Compartmental Design. Although these 4 picked determinants are amongst the most studied and essential in the field of HIV/AIDS, they do not have the capability and effectiveness to represent all other determinants and groups.

Figure 1
figure 1

Social determinants of health for HIV/AIDS stemmed from narrative evaluation.


Education is acknowledged as an essential social factor of health, being straight related to the socioeconomic advancement and wellness of people. Various instructional levels in a society result in financial variations and particularly health injustices. People with greater instructional levels, in basic, have much better task chances, a lower joblessness rate, much better financial conditions and, as a result, much better psychosocial conditions for decision-making about their ownhealth Therefore, education, within society, has an impact and influence on life span and its morbidities 24

For HIV/AIDS, education plays an essential function in minimizing its occurrence and frequency, particularly in low- and low-income nations. As lots of of the youths in establishing nations who go to school have not yet had sexual intercourse, education for these youths is important to the success of HIV/AIDS avoidance programs. At this time, it is possible to assist youths to postpone the start of their sexes, in addition to motivate the usage of protective approaches such as prophylactics 25 Petifor et al. (2016 ) 26 kept in mind that social defense programs, such as conditional money transfer to school participation, made girls remain in school longer, minimizing the threat of getting HIV. Additionally, education assists individuals to gain access to and comply with ART, in addition to assisting to minimize preconception, discrimination and gender inequality 27

Hardship and work

In Between the years 2020 and 2021, mainly as an outcome of the COVID-19 pandemic, the number of jobless individuals in the world increased from 187.3 million to 220.3 million, the biggest yearly boost in joblessness in this duration of time, reaching the rate average of 6.5% 28 Lots Of of these individuals who have actually lost their tasks have actually lost their only source of earnings, both individual and household, leading to an extreme decrease in labor earnings and a following boost in hardship. Compared to the year 2019, 108 million more employees are now thought about to be residing in hardship or severe hardship 29 A number of research studies have actually recorded the association in between joblessness and bad health status 30, 31, 32 Unemployed people, have their physical and psychological health impacted, most likely to experience anxiety, stress and anxiety, low self-confidence, demoralization, concern and physical discomfort 33 In addition, these people wind up having their understanding of health minimized, exposing themselves more to run the risk of of HIV infection, with threat habits such as exchanging sex for cash, typically with numerous partners and without prophylactics; low need for care and health services, and as a result hold-up in detection and initiation of treatment for HIV/AIDS and increase significant in death 34, 35

Alcohol and drug abuse

Alcohol and substance abuse, whether injectable or non-injectable, are fundamentally related to an increased threat of HIV infection. The primary element of injecting drugs is the sharing of syringes and needles, while alcohol and other types of drugs prefer the boost in dangerous habits due to the exchange of sex for drugs or cash, sexual disinhibition 36 Around 15.6 million individuals inject drugs worldwide, while around 2.8 million of those are dealing with the HIV infection 37 Sharing needles and syringes has the 2nd greatest possibility (of 10%) of HIV transmission per act, 2nd just to responsive anal sex. One in 160 individuals ends up being contaminated each time they share a syringe, with 10% of HIV cases in the U.S.A. being credited to this dangerous habits 38 In this method individuals who inject drugs (PWID) are exposed to the double path of contamination, sexual and intravenous. Another pertinent element is that drug abuse, alcohol intake, in addition to joblessness are aspects associated to minimized adherence to antiretroviral treatment 39 For that reason, the usage of alcohol and drugs is a SDH that needs to be thought about in the mathematical modeling of HIV/AIDS.

Prophylactic usage

Around 95% of cases, worldwide, of individuals being contaminated by HIV are credited to sexual practices without utilizing prophylactics. Prophylactics are the best understood, a lot of available and efficient approach to avoid HIV infection and other sexually sent infections, such as syphilis, gonorrhea and likewise some types of liver disease 40 Constant prophylactic usage can minimize HIV transmission amongst serodiscordant people by approximately 80% 41

Mathematical modeling

Compartmental design is a type of mathematical design that mimics the illness status of people within populations, which are divided into various compartments. Within each compartment, individuals are thought about uniform in terms of their habits and threat aspects 16, 17 The most generic and commonly utilized design is the SIR design, in which people are categorized into 3 types of compartments: Vulnerable (S), Contaminated (I) and Recuperated (R). Vulnerable people are those who have actually never ever had the illness or are most likely to end up being contaminated. After infection, these people move to the contaminated compartment and can spread out the illness to vulnerable people. The retrieved ones can establish life time resistance or go back to the Vulnerable compartment, depending upon the pathophysiology of the illness. In the case of HIV, the Recuperated compartment does not exist, as this illness has no remedy. Nevertheless, a variation of the SIR design for HIV is the replacement of the Recuperated compartment by the virally reduced compartment (T), where people in these compartments have an undetected viral load and their contribution to transmission is practically no 42 For this research study, we propose a prolonged design in which the population (N) is divided into Vulnerable (S), HIV-positive (I), Person with Help (A) and private virally reduced (T). Therefore, we think about the overall population (N), where N= S+ I+ A+ T. One method to design the characteristics of infection transmission is provided by the system of formulas:

$$ frac {dS} {dt} = kappa – mu S – beta frac {I} {N} S$$

$$ frac {dI} {dt} = beta frac {I} {N} S {+alpha} _ {1} T-rho I – {gamma} _ {1} I-mu I$$

$$ frac {dA} {dt} = rho I {+alpha} _ {2} T- {gamma} _ {2} A – {delta} _ {1} A-mu A$$

$$ frac {dT} {dt} = {gamma} _ {1} I+ {gamma} _ {2} A – {delta} _ {2} T- {alpha} _ {1} T- {alpha} _ {2} T-mu T$$

where ( kappa ) represents the population’s natality rate and ( mu ) the natural death rate (inverted of the typical life span). ( beta ) represents the efficient contact rate, I/N the portion of contaminated people. Therefore, the term ( beta frac {I} {N} ) represents the HIV transmission rate. After a duration ( {rho} ^ {-1} ), the contaminated private ends up being “full-blown help”. We think about that the private in class I, with the presumption that treatment happens, after a time ( {{gamma} _ {1}} ^ {-1} ) they reaches undetected viral load levels, the very same uses to the private in compartment A, in this case after a time ( {{gamma} _ {2}} ^ {-1} ) Nevertheless, if this private with an undetected viral load stops treatment, the viral load might increase, which might lead the private to class I (transmittable) and even to compartment A, with rates ( {alpha} _ {1} mathrm {and} ) ( {alpha} _ {2} ), respectively. We presumed that people in compartment A have HIV-related death, ( {delta} _ {1} ), in addition to for people in compartment T, ( {delta} _ {2} ) (with ( {delta} _ {2} < < {delta} _ {1} )). Figure 2 programs the epidemiological plan of the HIV/AIDS transmission design.

Figure 2
figure 2

Epidemiological plan of the HIV/AIDS transmission design.


One method to consist of the education element would be to integrate a brand-new compartment, signified here by (R-removed), representing people who through instructional projects alter their sexual habits so as not to be vulnerable to HIV transmission, as revealed by 42 Criterion ( {theta} _ {1} ) represents this habits. Nevertheless, these people can alter their habits once again and go back to infection vulnerability at a rate ( {theta} _ {2} ) The characteristics of this class is provided by the formula,

$$ frac {dR} {dt} = {theta} _ {1} S- {theta} _ {2} R-mu R$$

Remembering that as we included a brand-new compartment into the design, the overall population is now provided by N= S+ I+ A+ T+ R and the vulnerable characteristics is customized by consisting of the term ( {-theta} _ {1} S)

Prophylactic usage

To integrate the impact of prophylactic usage, we can include this element through the criteria ( varepsilon ) and ( nu ), which represent the prophylactic effectiveness and compliance, respectively. So, the item ( c= varepsilon nu ) represents the level of defense versus HIV through prophylactic usage 43 We customized the efficient contact rate, which goes as follows:

where ( 1-c) steps the failure to avoid transmission through prophylactic.

Alcohol and drug abuse

One method to integrate the substance abuse as SDH in a mathematical design is to limit the research study to this subpopulation, that is, think about a compartmental design in which all compartments relate to drug users 44 For example, Burattini et al. (1998 ) 45 revealed the effect of crack-cocaine usage on the frequency of HIV/AIDS amongst drug users. Alcoholic abuse can be included in the design reducing (or increasing) the criterion worths, which can be affected by alcohol usage. For example, the level of defense versus HIV through prophylactic usage (( c)) as

with ( {phi} _ {c} << 1), representing the alcoholic abuse impact. In the case of lack of alcoholic abuse impact in the mathematical design, we presume ( {phi} _ {c} =1.)

Hardship and joblessness

The addition of aspects such as hardship and joblessness can be used to a number of criteria in the design. Galanis and Hanieh (2021 ) 19 check out the usage of these aspects by customizing the transmission rate by a direct approximation of

$$ beta {(x} _ {1}, {x} _ {2}) = {beta} _ {0} + {beta} _ {1} {x} _ {1} + {beta} _ {2} {x} _ {2} $$

where ( {x} _ {1} ) and ( {x} _ {2} ) are the hardship and joblessness rates, respectively.

We can use this adjustment to criteria such as ( {alpha} _ {1} ), ( {alpha} _ {2} ), ( {gamma} _ {1} ) and ( {gamma} _ {2} ), as they can likewise be affected bysocial determinants Therefore, the design with the addition of the social determinants discussed here has the list below type:

$$ frac {dS} {dt} = kappa – mu S – (1-c) beta {(x} _ {1}, {x} _ {2}) frac {I} {N} S {-theta} _ {1} S+ {theta} _ {2} R$$

$$ frac {dI} {dt} =( 1-c) beta {(x} _ {1}, {x} _ {2}) frac {I} {N} S {+alpha} _ {1} T-rho I – {gamma} _ {1} I-mu I$$

$$ frac {dA} {dt} = rho I {+alpha} _ {2} T- {gamma} _ {2} A – {delta} _ {1} A-mu A$$

$$ frac {dT} {dt} = {gamma} _ {1} I+ {gamma} _ {2} A – {delta} _ {2} T- {alpha} _ {1} T- {alpha} _ {2} T-mu T$$

$$ frac {dR} {dt} = {theta} _ {1} S- {theta} _ {2} R-mu R$$

Mathematical simulation

Here, we provide an application of the design explained above. We fitted the design with information of brand-new cases and deaths of AIDS gathered from the Brazilian Health Ministry 46 We approximated the natural death rate and birth rate in order to the design approximate the overall population of Brazil in between 2003 and 2030. Table 1 programs the worths of criteria utilized in the simulations.

Table 1 Criterion description of the HIV/AIDS design.

Presuming the variety for each criterion displayed in Table 1, we carried out a level of sensitivity analysis utilizing an analytical variance-based approach 53 to assess the design criterion impacts in the characteristics of the all variables gradually. Considering that we thought about AIDS information for the calibration procedure, we provide in Fig. 3 the level of sensitivity analysis for the A compartment over 2003 to 2019. The most influent criterion, for the AIDS compartment, is the HIV transmission rate.

Figure 3
figure 3

Overall Sobol’ indices for the A compartment.

For this reason, we presumed the connection of hardship for just this criterion. The hardship rate was computed utilizing 3 National Home Studies (PNAD)–the routine PNAD, Continuous-PNAD, and PNAD-COVID for 2001– 2011, 2012– 2019, and 2020, respectively. After 2020, we presumed 2 various circumstances of hardship rate, circumstances of development and hardship decrease in between 2020 and 2030 (Fig. 4). We anticipate the HIV/AIDS occurrence and death rates (per 100,000 people), according to the level of hardship (Fig. 4).

Figure 4
figure 4

Hardship rate circumstances in between 2003 and 2030.

Figure 5 reveals that depending upon the level of hardship in the nation, in the future, we can anticipate of a boost (reduction) on these health results. This outcome programs the significance of governmental policies to hardship mitigation in order to minimize the occurrence and death of HIV/AIDS.

Figure 5
figure 5

HIV/AIDS occurrence and death rate under various circumstances of hardship in between 2003 and 2030.

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