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Impact assessment of selfmedication on COVID19 prevalence in Gauteng, South Africa, using an agestructured disease transmission modelling framework
BMC Public Health volume 24, Article number: 1540 (2024)
Abstract
Objective
To assess the impact of selfmedication on the transmission dynamics of COVID19 across different age groups, examine the interplay of vaccination and selfmedication in disease spread, and identify the age group most prone to selfmedication.
Methods
We developed an agestructured compartmentalized epidemiological model to track the early dynamics of COVID19. Agestructured data from the Government of Gauteng, encompassing the reported cumulative number of cases and daily confirmed cases, were used to calibrate the model through a Markov Chain Monte Carlo (MCMC) framework. Subsequently, uncertainty and sensitivity analyses were conducted on the model parameters.
Results
We found that selfmedication is predominant among the age group 1564 (74.52%), followed by the age group 014 (34.02%), and then the age group 65+ (11.41%). The mean values of the basic reproduction number, the size of the first epidemic peak (the highest magnitude of the disease), and the time of the first epidemic peak (when the first highest magnitude occurs) are 4.16499, 241,715 cases, and 190.376 days, respectively. Moreover, we observed that selfmedication among individuals aged 1564 results in the highest spreading rate of COVID19 at the onset of the outbreak and has the greatest impact on the first epidemic peak and its timing.
Conclusion
Studies aiming to understand the dynamics of diseases in areas prone to selfmedication should account for this practice. There is a need for a campaign against COVID19related selfmedication, specifically targeting the active population (ages 1564).
Introduction
In response to the outbreak and alarmingly rapid spread of COVID19 around the globe, health authorities implemented disease control strategies centered on nonpharmaceutical and pharmaceutical interventions. The effectiveness of these measures is partly dependent on available logistics and individual responses to such interventions. Owing to inadequate health promotionrelated resources and limitations in patient health literacy, selfmedication and the use of complementary medicine is a common global phenomenon and highly predominant in the global south [1,2,3,4,5,6,7]. Evidence of COVID19associated selfmedication is well documented in the literature (see for example, [8,9,10] and referenced articles thereof), and the reliance on selfmedication by segments of the global population hinders the effectiveness of the various interventions instituted by health authorities. This is because, most intervention measures do not consider the selfmedicated population since these cases often go unrecorded, leading to an oversight in the formulation of intervention policies. When measures are implemented without taking into account selfmedication, there is a risk of diluting the overall effectiveness of these efforts.
COVID19related health policies have benefited from several policydriven mathematical infectious disease models, where these models have helped shape policy frameworks in the quest to curb the spread of the disease, see, for example, works in [11,12,13,14,15,16]; also see [17, 18] for a good review on some of these models. Despite the large body of collections of policydriven mathematical disease models on this subject, there seems to be an inadequate study on mathematical disease modelinformed selfmedication dynamics. The works in [13, 19] are the few attempts to incorporate the dynamics of selfmedication into COVID19 mathematical models. Both studies show selfmedication dynamics has played a major role in the spread of COVID19, and that efforts should be intensified to put that in check. These works are based on Cameroon and Nigeria COVID19 cases, respectively. It is imperative that impact of age dynamics is incorporated in the modelling framework in that the literature demonstrates age as an important factor influencing selfmedication [9, 20, 21]. Among others, the limitations of the models presented in these studies are that impact of vaccination dynamics on the disease prevalence and age structure of the population were not considered in the modelling framework. In other words, the impact of selfmedication across different age groups on the dynamics of the disease transmission, and the interplay of vaccination and selfmedication on the spread of the disease were missing.
Selfmedication within the context of our proposed study is defined as any approach by an individual to treat the disease through the use of substances (e.g., herbal medicine or overthecounter drugs) or belief systems (e.g., faith) without consulting a certified professional for such a purpose. These treatments, in most cases, are not efficacious. Not only do they increase the likelihood of prolonged infectious periods of the disease, but they also hinder the isolation of these individuals as they do not make themselves available, thereby increasing the number of infectious individuals in the population. This, in turn, amplifies the force of infection within the population. Therefore, there is a need to incorporate this additional layer of dynamics into the disease modeling framework.
In view of the above, this paper proposes an agestructured mathematical COVID19 disease model that incorporates selfmedication. We considered the case where disease transmission coefficients are different across (age)groups with associated group specific contacts that map out the mixing pattern within and between these groups. We used case data from Gauteng, South Africa in our study. Gauteng has the largest share of the South African population, having approximately 15.5 million people (26.0%) living in the province [22]. A highly urbanised province having Johannesburg as its capital city. We addressed the following questions: (i) what is the impact of selfmedication on the spread and severity of COVID19 with or without vaccination? This question we address via the impact of the selfmedication on the effective reproduction number of COVID19. (ii) Which of the age groups has the highest incidence of selfmedication? We also assessed the sensitivity of the basic reproduction number, first epidemic peak, and first epidemic peak time, respectively, to model parameters (specifically parameters capturing selfmedication). We define the first epidemic peak as the first occurrence of the highest magnitude of the disease and the first epidemic peak time refers to the time duration of which we recorded the first highest magnitude of the disease.; the effective reproduction number is the average number of secondary cases per infected individual in the population comprising both susceptible and nonsusceptible hosts (in our case, vaccinated individuals) and the basic reproduction number is the effective reproduction number evaluated at the diseasefree steady state.
The rest of the paper is organized as follows: The model formulation, related assumptions, and remarks are discussed in “Method” section. The numerical simulations and relevant discussions are provided in “Results” section, where the model is estimated using Gauteng COVID19 age data, and sensitivity analysis of \(\mathcal {R}_0\) (and other model implied quantities) on selected model parameters are also conducted. Finally, the findings are summarized in “Conclusion” section.
Method
Model formulation
The schematic presentation of the proposed model is given in Fig. 1. The population is stratified into seven compartments: susceptible (\(S_i\)), vaccinated (\(V_i\)), exposed (\(E_i\)), infected (\(I_i\)), infected selfmedication (\(I^{sm}_i\)), infected formal treatment (\(I^{ft}_i\)) and removed (\(R_i\)). Individuals transition across these compartments in accordance with their disease status at each time period. These compartments are further stratified into age groups, for which we denote as i.
Susceptible individuals are individuals in the population that are susceptible to the disease; vaccinated are those individuals who have been vaccinated; exposed are those who have exposure to the disease; infected are those who have been infected by the disease and are exhibiting symptoms; infected selfmedicated and formaltreatment are those infected individuals who selfmedicate and those who seek formal treatment, respectively; removed compartment constitutes recovered individuals—this includes disease induced deaths.
Selfmedicated individuals are those who resort to any form of remedy to combat the disease, except using formal treatment. This can take the form of home remedies (examples, traditional or herbal medicines, overthecounter drugs, etc.), spiritual cleansing or prayers as recorded in some jurisdictions [13, 19], and others. These treatments in most cases are not efficacious; see for instance [23] and references therein. Not only does this increase the likelihood of prolonged infectious periods of the disease, it prevents isolation of these individuals as they do not make themselves available, therefore increasing the number of infectious individuals in the population, which will then amplify the force of infection within the population. consequently, the need to incorporate this additional layer of dynamic into the disease modelling framework. The formaltreatment compartment constitutes individuals who resort to treatment at a certified or government recognized health care space. We define treatment as the administration of drugs, or any other medication by healthcare professionals.
The disease system dynamics are as follows: we assume a short duration of the disease as in the case of a seasonal disease. The assumption of short duration of the disease pertains to the exclusion of demographic parameters and not related to infection parameters; we excluded population demographics such as birth and death rates in the modelling framework. Birth and natural death rates can be excluded from mathematical models when investigating disease dynamics occurring within few weeks or months. See , for example, works in [24,25,26,27,28,29,30]. Specifically, the works outlined in [25, 26, 28,29,30] provided COVID19 mathematical models excluding effects of birth and natural death rates. Mathematical models without demographic parameters have extensively been used to assess dynamics of disease epidemics. Models of this nature (epidemic models) are used to model rapid outbreaks that happens in less than a year [27].
Now, Observe that subscript i on model parameters corresponds to the parameters for each of the age groups and that those without subscript i imply that the parameter is the same across the age groups. Against this backdrop, the model assumes a per capita vaccination rate \(\nu\) (\(\nu S_i\) are vaccinated and enters \(V_i\)) and that vaccineinduced immunity lasts for the entire disease outbreak period. Here we assume that \(\nu\) is the same across all the age groups as we recognize that South Africa’s vaccination program commenced in February 2021 [31], implying the vaccination commencement date for Gauteng Province is not earlier done February 2021. The current study considers COVID19 infection period between March 1, 2020 and July 5, 2020there was no vaccination in place nor vaccination strategy. Our considered period is in line with the research questions we want to address: it serves as the base period to carry out sensitivity analysis on the study’s parameters of interest. Also, the proposed study is a generic study, not an empirical study, therefore assuming equal vaccination rates across the different age groups addresses the purpose of our study. We define vaccination under this setting as that which confers protection of individuals from the disease.
Individuals in \(S_i\) and \(V_i\) are infected with the disease at the respective rates of \(\mathcal {B}^s_i\) and \(\mathcal {B}^v_i\)—we assume that transmission is frequency dependent. \(\mathcal {B}^s_i S_i+\mathcal {B}^v_i V_i\) of individuals enter the exposed compartment \(E_i\). The latency rate for which individuals transition from \(E_i\) is \(\rho\). Thus, \(\rho E_i\) individuals transition from \(E_i\) to the infected compartment \(I_i\). We acknowledge that this assumption implies impact of disease transmissions is via \(\mathcal {B}^s_i\) and \(\mathcal {B}^v_i\).
Following the work in [13], we assume individuals are detected of the disease at the rate \(\alpha _i\). Consequently, we assume \(\alpha _i \theta _i I_i\) and \(\alpha _i(1 \theta _i) I_i\) number of individuals migrates from \(I_i\) to \(I^{sm}_i\) and \(I^{ft}_i\), respectively, where \(\theta _i\) is the proportion of those entering \(I^{sm}_i\) and \((1\theta _i)\) entering \(I^{ft}_i\). Finally, individuals are respectively removed from \(I_i,I^{sm}_i\) and \(I^{ft}\) at the rates \(\mu _i,\eta ^{sm}_i\) and \(\eta ^{ft}_i\). System 1 describes the evolution of the disease across the different compartments and age groups.
with initial condition
Force of infection \(\mathcal {B}^s_i\) and \(\mathcal {B}^v_i\) and reproduction number
Since the underlying framework of the proposed model and study is age structured, the disease force of infection (\(\mathcal {B}^s_i\) and \(\mathcal {B}^v_i\)), defined as the rate at which susceptible/vaccinated individuals become exposed, is group specific; this is influenced by the activities within and between groups, and is captured by the overall contact levels. The intensity of a group’s contact level influences the disease cases within the group and at the population level. Following the work in [32, 33], and related works in the field, we model the force of infection for a representative group as follows: Let \(x_{ij}\) be the average number of contacts per person per unit time in a representative group, where \(i=j\) is within group contact and \(i\ne j\) outside group contacts. The unit time could be day(s) or month(s) (this study considered daily number of contacts). This defines the contact matrix in the population. We assumed heterogeneous effective transmission coefficients across age structures; these are respectively denoted as \(\beta ^s_i\) and \(\beta ^v_i\) for susceptible and vaccinated individuals. \(\mathcal {B}^s_i\) and \(\mathcal {B}^v_i\) are expressed as
where we note that
\(N_j\) is the population size of the individuals across age group j for all disease compartments, n is the number of age groups, and \(0\le e \le 1\) captures the vaccine efficacy. Assuming proportionate mixing of individuals between groups. Observe that individuals in the formal treatment compartment are excluded from the expression for the force of infection; this is attributable to the assumption that Individuals in the formal treatment compartment are assumed to receive effective treatment such that their infectivity is reduced to a negligible level. The resulting general effective reproduction number from the model is derived as (See Supplementary Materials)
where \(x_i\) in Eq. 4 is the daily number of contacts made by an individual in group i per unit time. We note that the effective reproduction number is the average number of secondary cases per infected individual in the population comprising both susceptible and nonsusceptible hosts (in our case, vaccinated individuals). The basic reproduction number is the effective reproduction number evaluated at the disease free steady state. It is the average number of secondary infections produced by an infected individual in the population where everyone is susceptible. Observing Eq. (4) leads to the following remarks.
Remark 1
All other parameters held constant, the proportion of individuals who undergo self medication \(\theta _i\) positively relates to \(\mathcal {R}_t\) and \(\mathcal {R}_0\). Implying increasing \(\theta _i\) increases \(\mathcal {R}_t\) and \(\mathcal {R}_0\).
The epidemiological implication of Remark 1 is that the more number of people selfmedicate the more average number of secondary cases of the disease at time t in the population, thus to reduce the disease spread, a campaign against selfmedication may be effective.
Remark 2
All other parameters held constant, the detection rate (\(\alpha _i\)) negatively relates to \(\mathcal {R}_t\) and \(\mathcal {R}_0\).
Proof
The prove of Remark 2 can be shown by observing that the first partial derivative of \(\mathcal {R}_t\) (Eq. (4)) with respective to \(\alpha _i\) is negative for every value of \(\alpha _i\), thus \(R_t\) decreases as a function of \(\alpha _i\). \(\square\)
Remark 2 indicates, as a policy implication, increasing the detection rate of the disease can help curb its spread, when other parameters are held constant. Increasing detection rate can reduce disease incidence in the population.
Markov Chain Monte Carlo estimation scheme
Markov Chain Monte Carlo Delay Rejection Adaptive Metropolis [34] was used to estimate model parameters. We adopted the Matlab package mcmcrun provided in [35]. The model’s goodness of fit was assessed using the normalized mean square error (NMSE), as found in [13]. The likelihood function of the observed state, the number of new infections, is assumed as normal distribution and the prior distributions of the parameters are assumed as normally distributed. We started the estimation process from nonoptimized values; we did three runs of the algorithm, starting from the values of the previous run in order to locate the appropriate posterior distribution of the parameters. Each of the runs has 10,000 simulations, making 30000 simulations in total. We then estimated the mean from the individual final chains of the model parameters of interest.
Estimating contact matrix
We employed the approach used in [36,37,38] in estimating the contact matrix. We partitioned the Gauteng case data into the three age groups: 014, 1564, and 65+. This we did by noting that the case data is partitioned into age groups (010, 1110, 2130, 3140, 4150, 5160, 6170, 7180, 80+); and the age groups do not match appreciably with our proposed age groups for the study. Therefore, we estimated the cases in each age groups (014, 1564, and 65+) by first estimating the number of cases in, for example, the age group 1114, and then add that estimated number cases to the cases in age group 010 to arrive at the number of cases in 014. We do same for 1564, and 65+. As notational example, let \(C_{010}\) and \(C_{1120}\) be number of cases in age groups 010 and 1120 respectively, \(P_{1114}\) and \(P_{1120}\) be the respective population size of age group 1114 and 1120, then the number of cases for the age group 014 is given as
The estimated number of cases for each age group for our proposed age groups is then used as input in our estimation scheme. Note that, this approach assumes that cases are evenly distributed among the groups.
Results
Numerical analysis
This section discusses numerical analyses by first presenting the estimated values of the parameters not found in the literature. We based our estimation procedure on COVID19 cases in Gauteng, South Africa. Gauteng has the largest share of the South African population, having approximately 15.5 million people (26.0%) living in the province [22]. Table 1 presents the demographic of Gauteng by age range. Observe that age 1565 constitutes the largest population.
Data set on Gauteng COVID19 cases
The data set on Gauteng province COVID19 cases is now publicly available at: https://www.covid19sa.org/. The data set is a record of COVID19 cases on different disease age groups: 010, 1110, 2130, 3140, 4150, 5160, 6170, 7180, and above 80 (80+). We considered cases for the period spanning between March 1, 2020 and July 5, 2020, inclusive. For the purpose of our study we stratified the population into three age groups: 014, 1564, and above 65 (65+). This stratification is to group the population into active and nonactive subpopulations as well as dependent and independent subpopulations. We hereby assume individuals in ages 014 are dependent subpopulation and those in 1564 and 65+ are independent with regards to issues relating to self medication; the age group 1564 is the most active subpopulation.
Estimated contact matrix for Gauteng
We used South African’s population contact matrix to estimate that of Gauteng province, and is adopted from [38]; we used the synthetic contact matrix estimated in the paper, a decision informed by the fact the estimated contact matrix reflects COVID19 impact on the population social contact. The contact matrix is estimated as
where we used density correction approach for reciprocity correction. The graphical presentation of the contact matrix is given in Fig. 2. Observe that the Age group 1564 has the highest average number of within group contacts and age group 65 and above the least.
Model parameters estimation and numerical analysis
Recall the age structure Gauteng’s COVID19 case data is incompatible with the defined age structures for our studies—case data is partitioned into age groups (010, 1110, 2130, 3140, 4150, 5160, 6170, 7180, 80+). Our interest is to group the cases by age groups 014, 1564, and 65 and above. The estimated population age structure of Gauteng is grouped as 04, 59, 1014,1519, 2024,2529, 3034, 3539, 4044, 4549, 5054, 5559, 6064, 6569, 7074, 7579; see [22] for population demographics. This implies we need to estimate the population sizes of the age groups of interest. We first have to transform the COVID19 case agestructured data from (010, 1110, 2130, 3140, 4150, 5160, 6170, 7180, 80+) to (04, 59, 1014,1519, 2024,2529, 3034, 3539, 4044, 4549, 5054, 5559, 6064, 6569, 7074, 7579). And then group into 014, 1564, and 65 and above. We do this by borrowing the ideas from [39], outlined below:

i.
Suppose an observed data points \((x_j,y_j), j=1,2,...N\), where we define \(x_j\) in our setting as ages in 5 years intervals and \(y_j\), the cumulative population sizes for ages up to and including \(x_i\)

ii.
We can define a function f(x) that interpolates all points between each of the consecutive pair of knots \(x_j\) and \(x_{j+1}\).

iii.
After estimating the pairs \((x_j, y_j)\), we can then recover individual population estimates for each of the age groups by setting the population estimate for a representative age group \(x_j\) as \(y_{j+1}y_{j}\).
Figure 3 is the plot of the cumulative curve. It plots the the age and the cumulative population size. The dots in the figure are the cumulative population size obtained from [22]. The solid black and red lines connects the interpolated points (black dots) using the linear and spline interpolation schemes. Observe these interpolation schemes approximately coincide. For this reason, we used the estimated cumulative population sizes derived from the linear interpolation scheme for our analysis. We obtain the population size estimates for the required age groups using the method outlined above.
Figure 4 presents the plot of the estimated model for the three Age groups, and we see an appreciable fit (\(NMSE\approx 72.95\%\)). The grey region indicates 95% confidence bands of the estimated disease states, which we obtained by sampling the final respective chains of the parameters and using the resulting sample to calculate the predictive limit. The chain plots are presented in Fig. 5, and it shows generally appreciable convergence of the chains. Table 2 presents the values of model parameters not estimated and initial system state values. We set the value of the measure of vaccine efficacy e at 93% (this coincides with that of BNT162b2 (89.0% to 93.2%) [40]). The model implied estimates indicates that selfmedication is predominant among Age group 1564 (74.52%), followed by Age group 014 (34.02%); Age group 65+ records 11.41%.
Sensitivity analysis
This section discusses sensitivity analysis of the basic reproduction number \(\mathcal {R}_0\), first peak magnitude, and first epidemic peak time to model parameters respectively. The derivation of the \(\mathcal {R}_0\) is presented in the Supplementary Materials. We employed the Latin Hypercube Sampling Partial Rank Correlation Coefficient (PRCC) scheme [42, 43]. The PRCC is a measure of the strength of a linear association between the model parameters and model derived quantities or outputs (in our case, the \(\mathcal {R}_0\), first epidemic peak magnitude, and first epidemic peak time); the value is between \(1\) and \(+1\). We assumed a parameter range of values of \(\pm 50\) of the values of the parameters of interest, presented in Table 3.
Figure 6 is the visualization of the degree of the sensitivity of \(\mathcal {R}_0\), first peak epidemic, and first epidemic peak time to selected model parameters . We observed that \(\mathcal {R}_0\) has high degree of correlation with \(\alpha _1,\theta _2\), \(\beta ^s_1\), and \(\beta _2^s\)–see Fig. 6a; the First epidemic peak of the disease is strongly correlated with \(\alpha _2\), \(\theta _2\), and \(\beta _2^s\)—see Fig. 6b; and the first epidemic peak time is strongly correlated with \(\alpha _2,\theta _2,\beta ^s_2\). Table 4 present a summary of the abovementioned observations. In the interest of our study, the policy parameters of interest are the proportions of individuals who selfmedicate across the various age groups—\(\theta _1,\theta _2\) and \(\theta _3\), and vaccination rate \(\nu\). We note that \(\theta _2\) has the most impact on \(\mathcal {R}_0\), First Epidemic Peak, and First Epidemic Peak Time.
Figure 7 presents the respective histograms of \(R_0\), First Epidemic Peak, and First Epidemic Peak Time, with their respective means. The average \(R_0\) is 4.16499, and that of First Epidemic Peak and First Epidemic Peak Time are 241,715 and 190.375, respectively.
The contour plots in Fig. 8 demonstrates the joint impact of selfmedication and vaccination on the effective reproduction number, and thus the spread of COVID19. The figure shows that the joint impact of selfmedication \(\theta\) and vaccination \(\nu\) on the spread of the disease is negligible — the value combinations of \(\theta\) and \(\nu\) for which \(\mathcal {R}_t\) is above 1 corresponds to negligible values of \(\nu\). We note that effective vaccination coverage is crucial in reducing the spread of the disease; selfmedication plays a vital role in the spread of the disease in the event of little to no effective vaccination coverage — range of values of the proportion of the selfmedicated population yielded \(\mathcal {R}_t\) above 1 (see Fig. 8a, obtained by assuming an equal variation of \(\theta\) across the different population groups).
Figure 8bd show the effect of the proportion of selfmedicated individuals in each population group and vaccination per capita on the effective reproduction number (\(\theta _i\) vs \(\nu\), \(i=1,2,3\)). We observe that among the age groups selfmedication activities corresponding to age group 1564 results in the highest value of \(\mathcal {R}_t\) in the event of little to no effective vaccination coverage. Thus, this group should be a target for public campaign against selfmedication. The effective reproduction number used here is the average for the entire period (from 1 to 127, consistent with case data used for parameter estimation) for each parameter value combination of \(\theta\) and \(\nu\). The computation process is outlined in Section 3 of the Supplementary Materials.
Discussion
Selfmedication and the use of complementary medicine is an integral component of disease treatment globally [1,2,3,4,5,6]. It is an alarming problem among resource limited countries in the global south. Even though selfmedication has the potential of reducing health care expenditure [44], it has its own associated cost, among which, is the dampening effect it has on health policy interventions towards the control of infectious diseases. Selfmedication as applied in our context of study can range from having faith that one will heal from the disease without ingesting any form of medicines to application of herbal medicine or over the counter drugs. Individuals who undergo selfmedication in most cases do not use efficacious treatments. Not only does this increase the likelihood of prolonged infectious periods of the disease, it prevents isolation of these individuals as they do not make themselves available, therefore increasing the number of infectious individuals in the population, which will then amplify the force of infection within the population. As pointed out in [13], selfmedication is a vital factor contributing to the spread of the disease although frequently overlooked; it contributes to the spread and severity of the disease and the population of individuals who under selfmedication heightens the disease persistence against eradication.
This study proposed an agestructured mathematical disease model that incorporates selfmedication in its dynamics; and used COVID19 case data from Gauteng Province, South Africa, for analysis. We conducted uncertainty and sensitivity analysis on the model implied quantities—basic reproduction number, first epidemic peak, and first epidemic peak time—to the model parameters. The respective means of these quantities are 4.16499, 241,715, and 190.376. The model estimated proportion of individuals who selfmedicated shows that selfmedication is higher among age group 1464 than the other age groups (014 and 65+). Also, the sensitivity analysis indicated that among the three age groups, age group 1564 selfmedicated activities has the most impact on the basic reproduction, first epidemic peak, and first epidemic peak time. Further analysis shows that selfmedication is a vital factor impeding control of the disease in the absent of effective vaccination, however, has negligible joint impact on the disease with effective vaccination coverage. This we demonstrated by assessing the joint impact of the selfmedication and vaccination on the average effective reproduction number. These findings show that in the case of Gauteng province, the active population (age group 1564) have the highest level of selfmedication incidence; (ii) selfmedication is a crucial factor hindering control of the disease; (iii) selfmedication joint impact with effective vaccination coverage on the spread of COVID19 is negligible.
A weakness of our study is that, the proposed model used to address the research questions does not account for population demographics such as birth and death rates. Studies integrating this population demographics can provide that additional insight into addressing the research questions outlined in this paper. The method used to estimate the disease incidence cases for a given age group where such a group has no record cases assumes that cases are evenly distributed among the age groups. This assumption could either overestimate or underestimate the incidence cases in a representative group. Future work could address these gaps in our study.
Conclusion
We addressed three research questions using Gauteng province, South Africa, COVID19 cases spanning from the periods March 1, 2020 to July 5, 2020: (i) what is the impact of self medication across different age groups on the dynamics of the disease (example, disease prevalence)? (ii) what is the effect of the interplay of vaccination and selfmedication on the spread of the disease? and (iii) which of the age groups has the highest incidence of selfmedication? Using Gauteng province COVID19 cases from the period March 1, 2020 to July 5, 2020, we have demonstrated that selfmedication plays a crucial role in combating COVID19, and that regardless of the level of effectiveness of instituted vaccination programs, it must be put in check. Appropriate campaign against COVID19 related selfmedication is justified. It is also worth noting that campaigns should target the active population (ages 1464).
Availability of data and materials
The data is publicly available at: https://acadic.org/southafrica/.
Abbreviations
 ACADIC:

AfricaCanada Artificial Intelligence and Data Innovation Consortium
 ODEs:

ordinary differential equations
 MCMC:

Markov Chain Monte Carlo
 NMSE:

Normalized mean square error
 \(\mathcal {R}_0\) :

Basic reproduction number
 \(\mathcal {R}_t\) :

Effective reproduction number
 \(S_i\) :

Susceptible population in age group i
 \(V_i\) :

Vaccinated population in age group i
 \(E_i\) :

Exposed population in age group i
 \(I_i\) :

infected population in age group i
 \(I^{sm}_i\) :

infected and selfmedicating population in age group i
 \(I^{ft}_i\) :

infected population obtaining formal treatment in age group i
 \(V_i\) :

Removed population in age group i
 \(C_{ij}\) :

Number of cases in age groups \(ij\)
 \(P_{ij}\) :

Population size of age groups \(ij\)
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Acknowledgements
We will like to thank the Provincial Government of Gauteng for providing us with the data for the studies. JDK acknowledge support from IDRC (Grant No. 109981), NSERC Discovery Grant (Grant No. RGPIN202204559), NSERC Discovery Launch Supplement (Grant No: DGECR202200454) and New Frontier in Research Fund Exploratory (Grant No. NFRFE202100879).
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The findings and conclusions in this report are those of the authors and do not necessarily represent the official position of their respective institutions. The authors declare no conflict of interest.
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This research is funded by Canada’s International Development Research Centre (IDRC) (Grant No. 109559001).
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Conceptualization: JDK, WSA; methodology: WSA, JDK, BM, QH, WAW; software: JDK, BM; validation: all authors; investigation: WSA, QH, JDK; resources: JDK, A. Asgary, JW, BM, JO; data curation: WSA; writingoriginal draft preparation: WSA, JDK; writing review and editing: all authors; visualization: WSA, JDK; supervision: JDK, NB, A. Asgary, A. Ahmadi, JO, JW, BM; project administration, JDK; funding acquisition: JDK, A. Asgary, JO, JW.
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The Ethics approval to use the data was deemed unnecessary according to national legislation. In the context of South Africa, collecting data in hospitals does not require ethical review and approval. The administrative approval to access the raw anonymized data, analyze it, and use it for publication was given by the Provincial Government of Gauteng. The premier office is represented by Prof. Bruce Mellado who is a coauthor of the manuscript. All methods were carried out in accordance with relevant national and international guidelines and regulations.
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Avusuglo, W.S., Han, Q., Woldegerima, W.A. et al. Impact assessment of selfmedication on COVID19 prevalence in Gauteng, South Africa, using an agestructured disease transmission modelling framework. BMC Public Health 24, 1540 (2024). https://doi.org/10.1186/s1288902418984y
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DOI: https://doi.org/10.1186/s1288902418984y