A study of trend and pattern of HIV/aids disease in India using growth curve models

Introduction

Human life is surrounded by many ugly deadly diseases and some of them are only prevention without cure and one among them is Human Immunodeficiency Virus (HIV). HIV is a virus that takes over certain immune system cells to make many copies of it. HIV causes slow but constant damage to the immune system. AIDS stands for Acquired Immune Deficiency Syndrome. AIDS is the condition diagnosed when there are a group of related symptoms that are caused by severe HIV infection or in layman's term AIDS is the latter stage of HIV. HIV is transmitted through four body fluids: blood, semen, vaginal fluid, and breast milk. In order to pass HIV from one person to another, HIV-infected fluid from one person needs to get into the bloodstream of another person. HIV is usually transmitted through sharing needles, unprotected anal, vaginal, and sometimes oral sex, and from mother to infant before or during delivery or while breastfeeding. Estimated HIV prevalence of adults in the age group between 15-49 years has declined in India. Epidemic was very high in 2000 that is it is 0.55% in 2000 and it is declined to 0.32% in 2010 and 0.21 in 2022. The state wise HIV prevalence in India shows the highest prevalence is observed in northeast region, the state Mizoram (2.70%), 1.36% in Nagaland and 1.05% in Manipur followed by Southern states namely Andhra Pradesh (0.67%), Telangana (0.47%) and Karnataka (0.46%). In India, the estimated number of People Leaving with HIV (PLHIV) is 24 lakhs. The highest number of PLHIV is in southern states namely Maharashtra, Andhra Pradesh and Karnataka. In India the estimated Annual New Infection (ANI) are nearly 62,970 in 2021, around 46.3% decline in ANI at National level in 11 years (2010-2021).

Declining trend is observed in most of the states. Rapid decline from 2010-2021 in three states viz. Himachal Pradesh(73%), Tamil Nadu (72%) and Telangana (71%) and increasing trend is estimated in Northeastern states-Tripura, Meghalaya, Arunachal Pradesh, Assam, Sikkim, Mizoram, and the Union Territory of Dadra and Nagar Haveli and Daman and Diu. There are 41970 estimated AIDS related deaths in India in 2021. A decline of 76.5% AIDS deaths from 2010-21. The declining trend is observed in all States/UTs excluding Puducherry, Arunachal Pradesh, Meghalaya, and Tripura. The highest decline in AIDS-related death (ARD) is estimated in Chandigarh, Telangana, and West Bengal. Prevention of mother-to-child transmission of HIV (PMTCT) need are estimated at 20,612 in 2021 in India. Top 3 states accounting for the highest need are Maharashtra (12.9%), Bihar (11.9%) and Uttar Pradesh (10.6%) (NACO, (2022)) [1] . In this paper an analysis of the trend and pattern of morality of HIV/AIDS disease with indictors like prevalence rate, incidence rate and deaths (in lakhs) in India in the specified duration 2000-2021 is considered. This paper consists of five sections: Introduction about the study is given in the first section, second section deals with review of literature, methods and materials is given in third section, forth section contains Results and discussions of data and final section concludes the study. India has one of the largest HIV/AIDS populations globally, making it essential to track mortality trends to assess public health interventions. In the epidemic's early stages (1980searly 1990s), HIV spread rapidly among high-risk groups like sex workers, IDUs, and MSM due to limited awareness and healthcare infrastructure, raising mortality rates. (Panikar, 1992) [2] . NACO (1995) [3] later emphasized the need for a national program. ART introduction under the National AIDS Control Programme in 2004 helped reduce mortality, though challenges like late diagnosis persisted Basu et al. (2006) [4] ; Lanjewar (2007) [5] . Jha et al. (2007) [6] noted regional disparities in HIV/AIDS mortality, with southern states like Tamil Nadu and Andhra Pradesh seeing declines due to better healthcare, while northern states struggled with rising deaths from limited ART access and stigma. Solomon et al. (2008) [7] reported significant mortality declines in Tamil Nadu, aided by strong public health support. John et al. (2014) [8] found similar declines in Karnataka's urban areas, though rural areas still faced higher mortality due to limited healthcare and stigma. Growth models are crucial for tracking the HIV/AIDS epidemic, forecasting trends, and guiding policy. These models, ranging from simple exponential or logistic to complex compartmental forms, depict how HIV/AIDS cases evolve over time. In the early epidemic in India, exponential models predicted a rapid rise in cases due to limited awareness and treatment. Mann et al. (1992) [9] used this model to warn of uncontrolled spread without intervention, while Godbole and Mehendale (2005) [10] showed that as public health measures improved, exponential models began overestimating long-term trends. Kumar et al. (2008) [11] used a logistic growth model to project HIV in India, while Gupta et al. (2012) [12] extended it to show slowing growth in high-prevalence states like Maharashtra due to ART and prevention efforts. Sharma and Narain (2017) [13] applied the Gompertz model, highlighting regional differences in prevalence decline. For short-term projections, Tripathi et al. (2013) [14] used a polynomial model to capture fluctuations in incidence but noted its limitations for long-term forecasts. Desai et al. (2014) [15] explored nonlinear models to account for erratic incidence patterns in specific regions. Patel et al. (2019) [16] enhanced HIV incidence predictions in India by integrating machine learning with logistic growth models, showing that real-time ART and risk behaviour data improved accuracy. Rani et al. (2021) [17] combined the Gompertz model with socioeconomic data to project the impact of future public health interventions on the epidemic.

Methods and Materials

The data on prevalence rate, incidence rate and deaths (in lakhs) due to HIV/AIDS disease is collected from NACO for India in the form of time series data from 2000 to 2021. NACO (2021) [18] Exponential, Logarithmic and Polynomial Growth models and Growth rates are used to study the trend and pattern behaviour of HIV/AIDS disease. Growth models are used to describe and predict how a particular quantity changes over time. They are widely applied in various fields, including Epidemiology, Economics, Biology, and Sociology. In the context of disease prevalence, incidence, and mortality rates (like for HIV/AIDS), growth models help to analyze trends and forecast future behaviour. For our study we applied the models viz. Exponential growth model, Logarithmic growth model and Polynomial of order 3 to fit the data on prevalence rates, incidence rate, and mortality.

Growth rates: Growth rates are key metrics used to measure how quickly or slowly a quantity (e.g., population, disease prevalence, economic output) changes over time. In the context of epidemiology and public health, growth rates are essential for understanding the spread of diseases such as HIV/AIDS. Here is an overview of exponential growth rate and growth models used in our study:

Exponential Growth Rate

Exponential Growth Model:

The general equation for exponential growth model is 𝑦(𝑡) = 𝑦 0 𝑒 𝑟𝑡 where:  𝑦(𝑡) is the value of the quantity at time t.  𝑦 0 is the initial quantity at time t=0.  r is the decay constant, which represents the rate of decay.  t is the time.

Logarithmic Growth Model:

The general form of a logarithmic growth model is:

where:  y represents the dependent variable (e.g., mortality rate or case count),  t is the independent variable (e.g., time or a relevant predictor),  a and b are constants,  ln (𝑡) is the natural logarithm of t.

Polynomial of order 3 (Cubic Polynomial Model):

The general form of a cubic polynomial model is:

where:  Y is the dependent variable at time t,  t is time (e.g., in years),  𝑏 0 , 𝑏 1 , 𝑏 2 , 𝑎𝑛𝑑 𝑏 3 are the coefficients to be estimated.

Results and Discussions 3.1 Growth Rate of HIV/AIDS

The growth rate of HIV/AIDS in India can be examined through three indicators, such as prevalence, incidence, and mortality rates, as well as trends over time. The HIV/AIDS epidemic in India started in the early 1980s, with the first case reported in 1986. By the mid-1990s, HIV had spread rapidly, especially among high-risk groups such as commercial sex workers, intravenous drug users, and men having sex with men. In the 1990s, the annual number of new infections was growing exponentially, with HIV spreading quickly from urban areas to rural regions. The mortality rate was initially low, as HIV progressed to AIDS after several years. However, by the end of 1990s, AIDS-related deaths increased significantly due to limited access to antiretroviral therapy (ART). In 2021, the prevalence of HIV remained stable at around 0.2-0.3%. However, a Post-Pandemic Era because the COVID-19 pandemic disrupted HIV services in some areas, leading to concerns about temporary setbacks in testing and treatment coverage. The incidence of new HIV infections showed a decline, but the rate of reduction slowed down in some areas due to pandemic-related service interruptions. AIDS-related deaths continued to decline, although some disruptions during the pandemic raised concerns about temporary increases in mortality among untreated populations. India has witnessed a declining growth rate in terms of new HIV infections, prevalence, and mortality due to sustained government efforts, community-based interventions, and the scale-up of ART. However, disparities remain in some regions and populations, requiring ongoing focus and resources to sustain and improve these gains.

Growth Models of HIV/AIDS

HIV/AIDS incidence rate in India is observed from NACO report from 2000 to 2021. The data revels that in 2000 incidence rate was 0.18 and it is declined to 0.05 in 2021, which shows that there is sharp decline for the span of 21 years that is the decline was 72% (see Table 3). Two growth curve models namely exponential growth model and Logarithmic growth curve model are applied to study the growth pattern of the incidence rate. The results shows that estimated value of exponential growth curve is very close to observed value (Fig. 1). Furthermore, the Relative Absolute Error (RAE) for the exponential model was 0.157, reflecting a total absolute error that is only 15% of that of a naive model, whereas the logarithmic model's RAE was significantly higher at 0.281. The Relative Root Square Error (RRSE) followed a similar pattern, with the exponential model scoring 0.179 and the logarithmic model 0.292, underscoring the exponential model's superior fit to the data. Finally, the R-squared (R²) value for the exponential model was an impressive 0.96, indicating it explained 96% of the variance in incidence rates, compared to 0.91 for the logarithmic model. Collectively, these metrics highlight the exponential growth model's ability to more accurately capture and predict trends in incidence rates. The prevalence rate is estimated by two growth curves namely exponential and logarithmic growth curves. The analysis shows that there is 47. 5% declines from 2000 to 2021. The parameters of the models are estimated by the method of least squares. The analysis shows that the exponential curve shows good fit since the estimated values are nearer to observed values. The deaths due to HIV / AIDS and their estimated value using two growth curves, Polynomial and logarithmic curve are presented in Table 7. The analysis of the data shows deaths due to HIV/AIDS is declined by 75.6% from 2000 to 2021.

The polynomial curve shows good fit as its estimated value is collinear to observed number of deaths but logarithmic model shows very poor fit.

Conclusion

Analyzing HIV/AIDS using growth rates provides a comprehensive view of how the epidemic evolves over time. Prevalence, incidence, and mortality growth rates offer critical insights into the effectiveness of interventions and the status of the disease in different regions and populations. By closely monitoring these rates and adapting strategies accordingly, public health officials can make informed decisions to reduce the burden of HIV/AIDS and move towards achieving global health goals for HIV/AIDS eradication or control. The comparative analysis of the exponential and logarithmic growth models for predicting HIV/AIDS incidence rates consistently shows that the exponential model outperforms the logarithmic model across all metrics. The exponential model's lower MAPE, MALPE, MAE, RMSE, RAE, and RRSE values, combined with its higher R², demonstrate its superior predictive accuracy and reliability. This suggests that the exponential model is better suited for modeling HIV/AIDS incidence rates, offering more precise and consistent predictions. Similarly, when comparing the exponential and logarithmic growth models, the exponential model proves to be more effective in predicting HIV/AIDS prevalence rates. Its superior performance in terms of lower MAPE, MALPE, MAE, RMSE, RAE, and RRSE values, along with a higher R-squared, indicates that the exponential model is better at handling variance and outliers. This makes the exponential model a more reliable tool for public health officials, aiding in more accurate planning and intervention strategies for HIV/AIDS control. In the case of HIV/AIDS mortality, the polynomial growth model also proves to be more effective than the logarithmic model.

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