

ORIGINAL ARTICLE 

Year : 2022  Volume
: 9
 Issue : 3  Page : 7985 

Death probability analysis in the old aged population and smokers in India owing to COVID19
Parikshit Gautam Jamdade^{1}, Shrinivas Gautamrao Jamdade^{2}
^{1} Department of Electrical Engineering, Pune Vidyarthi Grihas College of Engineering and Technology, Pune, Maharashtra, India ^{2} Department of Physics, Nowrosjee Wadia College, Pune, Maharashtra, India
Date of Submission  22Mar2022 
Date of Acceptance  28Sep2022 
Date of Web Publication  22Dec2022 
Correspondence Address: Parikshit Gautam Jamdade Department of Electrical Engineering, Pune Vidyarthi Grihas College of Engineering and Technology, Pune, Maharashtra, India, Pune  411 052, Maharashtra India
Source of Support: None, Conflict of Interest: None
DOI: 10.4103/RID.RID_22_22
OBJECTIVE: Research has shown that older people and smokers have a higher death probability from coronavirus disease 2019 (COVID19). Thus, we investigated the effect of COVID19 on death probability for individuals aged 65–70 years and smokers in India. MATERIALS AND METHODS: We did so using a differential learning (feedbackward) model. In the present study, we examined World Health Organization (WHO) declared COVID19 data of India. We divided the patients into two groups accordingly: the population aged 65–70 years and female or male smokers. RESULTS: We observed that in the early stages of infection (up to 5 days), there was higher death probability in the older population; among smokers, it occurred in the middle period after infection (5–8 days). We estimated that the death probability among smokers was 1.905 times that of the older population. CONCLUSION: As Government of India, taking various initiatives to curb the spread of COVID19, but these are not enough, so we suggest measures that should help to reduce COVID19 infection in India.
Keywords: COVID19, death probability analysis, India, old aged population, Smokers
How to cite this article: Jamdade PG, Jamdade SG. Death probability analysis in the old aged population and smokers in India owing to COVID19. Radiol Infect Dis 2022;9:7985 
How to cite this URL: Jamdade PG, Jamdade SG. Death probability analysis in the old aged population and smokers in India owing to COVID19. Radiol Infect Dis [serial online] 2022 [cited 2023 Feb 3];9:7985. Available from: http://www.ridiseases.org/text.asp?2022/9/3/79/364770 
Introduction   
As of 2022, India has a population of almost 1.38 billion. Around 60% of the population lives in cities and highdensity areas. The Indian government confirmed the country's first case of coronavirus disease 2019 (COVID19) on January 30, 2020. To combat the spread of the disease, the government undertook various measures, including a nationwide lockdown and closure of all educational institutions, industrial, and commercial establishments from 25 March to June 22, 2020. During the lockdown, India's economy lost over US$4.5 billion a day. The most affected states in India were Maharashtra, Delhi, Tamil Nadu, Karnataka, Andhra Pradesh, Gujarat, Rajasthan, West Bengal, and Haryana.
The World Health Organization (WHO) declared COVID19 a pandemic on March 11, 2020. The pandemic spread daily.^{[1]} Large populated areas with a mobile population were severely affected.^{[2]} Reducing the transmission rate of COVID19 is very demanding. The WHO affirmed that COVID19 is a public health emergency owing to the great rise in confirmed cases.^{[3]} Projecting the spread of COVID19 is very difficult owing to limited data for determining the growth trajectory; such a projection would allow affected countries to respond to the pandemic. Various statistical distribution models have been used to make such forecasts;^{[4],[5],[6],[7],[8],[9],[10],[11],[12]} they could be used to define the spread of COVID19. Confirmed case data for COVID19 became available on the WHO site on December 31, 2021; they include information about total COVID19 cases, death rate, life expectancy, and death probability. That information is useful for health organizations attempting to mitigate the spread of COVID19.^{[13],[14],[15]}
Little research has examined the impact of COVID19 on death probability for populations aged 65–70 years and among smokers. Investigations have found that older individuals and smokers have higher death probability in epidemics; those studies explain the impact of COVID19 on the lungs and other organs.^{[16],[17],[18]} In the present study, we examined the impact of COVID19 on death probability for individuals aged 65–70 years and on smokers using a differential learning (feed backward) model to evaluate the change in death rate and life expectancy.
Differential Learning Model   
We developed a differential learning (feedbackward) model to simulate the spatial spread of death probability: age – COVID19 death rate / age – COVID19 life expectancy (ACDR / ACLE) system or smoker – COVID19 death rate / smoker – COVID19 life expectancy (SCDR / SCLE) system. The characteristics of this system are described by the secondorder differential equation as given by Newton's Second Law:
where x is the change in the COVID19 death rate or life expectancy from zero, u is the function of COVID19 death probability (whose response depends on COVID19 death rate or life expectancy), m is the COVID19 death rate or life expectancy, c is the population aged 65 years or female smokers, and k is the population aged 70 years or male smokers.
A block diagram of this system appears in [Figure 1]. Three physical parameters m, c, and k are not known accurately so we can assume that their values are within certain, known intervals.  Figure 1: Block diagram of the ACDR/ACLE System OR SCDR/SCLE System with Uncertain Parameters. ACDR/ACLE = Age – COVID19 death rate/age – COVID19 life expectancy, SCDR/SCLE = Smoker – COVID19 death rate/smoker – COVID19 life expectancy
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m = m (1 + p_{m} δ_{m}), c = c (1 + p_{c} δ_{c}), k = k (1 + p_{k} δ_{k})
where m, c, and k are the called nominal values. p_{m}, p_{c}, and p_{k} and δ_{m}, δ_{c}, and δ_{k} represent the possible variations on these three parameters.
According to Indian government data, 20%–30% of the country's population is aged 65 years and comprises female smokers; 30%–40% is aged 70 years and comprises male smokers. Of the population with COVID19 infection, for individuals aged 65–70 years and smokers, the COVID19 death rate/life expectancy was 40%–50%. Thus, in the present study, we took p_{m} = 0.4, p_{c} = 0.2, p_{k} = 0.3 and − 1≤ δ_{m}, δ_{c}, δ_{k} ≤1. This represents up to 40% uncertainty in the COVID19 death rate/life expectancy, 20% uncertainty in the population aged 65 years and female smokers, and 30% uncertainty in the population aged 70 years and male smokers.
The system model of LFT with real perturbations δ_{m}, δ_{c} and δ_{k} appears in [Figure 2] and [Figure 3] with the inputs and outputs of δ_{m}, δ_{c} and δ_{k} as y_{m}, y_{c}, y_{k} and u_{m}, u_{c}, u_{k}, respectively. The quantity 1/m appears as a linear fractional transformation (LFT) in δ_{m}  Figure 2: Block diagram of the ACDR/ACLE System OR SCDR/SCLE System. ACDR/ACLE = Age – COVID19 death rate/age – COVID19 life expectancy, SCDR/SCLE = Smoker – COVID19 death rate/smoker – COVID19 life expectancy
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 Figure 3: Input / Output Block Diagram of the ACDR / ACLE System OR SCDR / SCLE System
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with
On the same basis, the parameter c = c (1 + p_{c} δ_{c}) was represented as an upper LFT in δ_{c}
c = F_{U} (M_{c}, δ_{c})
with
and the parameter k = k (1 + p_{k} δ_{k}) was represented as an upper LFT in δ_{k},
k = F_{U} (M_{k}, δ_{k})
with
The system model of LFT with real perturbations δ_{m}, δ_{c}, and δ_{k} appears in [Figure 3] with the inputs and outputs of δ_{m}, δ_{c}, and δ_{k} as y_{m}, y_{c}, y_{k}, and u_{m}, u_{c}, and u_{k}, respectively, as shown in [Figure 1].
By doing the above substitutions, the equations can be related to all inputs with their corresponding outputs with perturbed parameters and represented as
u_{m} = δ_{m}y_{m}
u_{c} = δ_{c}y_{c}
u_{k} = δ_{k}y_{k}
By eliminating the variables v_{c} and v_{k}, the system dynamic behavior is given as
Let G_{mds} shows the COVID19 transmission state space matrix (CTSSM) (input/output dynamics) of the ACDR/ACLE system OR SCDR/SCLE system, which takes into account the uncertainty of parameters as shown in [Figure 4]. G_{mds} has four inputs (u_{m}, u_{c}, u_{k}, and u), four outputs (y_{m}, y_{c}, y_{k}, and y), and two states (x_{1} and x_{2}).  Figure 4: COVID19 death probability with change in COVID19 death rate for 65–70 aged populations
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The CTSSM of G_{mds} is given as
where
C_{2} = [1 0]
D_{21} = [0 0 0]
D_{22} = [0 0]
Here, G_{mds} depends only on m, c, k, p_{m}, p_{c}, p_{k} and on the original differential equation connecting y with u. Hence, G_{mds} is known with no uncertain parameters.
Thus, the differential learning model (feed backward) model represents death probability in terms of the COVID19 death rate and COVID19 life expectancy. We divided the patients into two groups according to the population of (1) aged 65–70 years and (2) female or male smokers. The observed variables were expressed as average values, the standard deviation (SD) and kurtosis as the median interquartile range (IQR), and the depending factors, COVID19 death rate, and COVID19 life expectancy had separate rates of variation.
Effect of Death Rate and Life Expectancy on Death Probability   
Research has shown that the COVID19 death rate and COVID19 life expectancy mainly depend on patients' conditional health and medical factors. They are mainly as follows: cardiovascular disease, chronic obstructive pulmonary disease, diabetes, malignancy, chronic liver disease, renal liver disease, hypertension, tuberculosis, white blood cell count, neutrophil count, lymphocyte count, platelet count, blood urea nitrogen (mmol/l), Creactive protein (mg/L), cytokines, interleukin6 (pg/ml), PaO_{2}/FiO_{2}, multilobular, albumin (g/L), alanine aminotransferase (U/L), aspartate aminotransferase (U/L), total bilirubin (mmol/L), and lactate dehydrogenase (U/L).^{[3],[6],[16],[17],[18]} According to the WHO, 5.989% and 3.414% of India's population were aged 65 and 70 years, respectively; 1.9% and 20.6% were female and male smokers; the COVID19 death rate and COVID19 life expectancy were 282.28% and 69.66%.
In the present study, we examined the spatial spread of death probability due to COVID19 for the population aged 65–70 years and female or male smokers. For the population aged 65–70 years, we modeled value variations by considering 40%, 20%, and 30% uncertainty with respect to the COVID19 death rate or COVID19 life expectancy, the population aged 65 years, and that aged 70 years, respectively. In our plots, the red lines indicate the designated value change for the COVID19 death rate or COVID19 life expectancy and the blue lines indicate the modeled value variations. The modeled values show the upper and lower bounds of variation in the COVID19 death rate or COVID19 life expectancy.
Our simulation results showed that at a 0.1 value (black lines) of an initial change in the COVID19 death rate and the death probability increased rapidly in individuals aged 65–70 years (blue lines). If that population sustained that death probability with no health deterioration, the survival probability would increase with further change in the COVID19 death rate: that would indicate immunity development against COVID19. The distribution probability plot indicates that the range of change in death rate (black lines) resulted in a major change in death probability (blue lines): 0.1–0.2 (black lines). The modeled values (black lines) varied from 0.1 to 0.4 on a log scale; they showed the maximum value of death probability (blue lines) on a linear scale [Figure 3].
At a 0.1 initial change in COVID19 life expectancy (black lines), there was 60% survival probability for individuals aged 65–70 years (blue lines). The COVID19 death probability reached a maximum value of 80% (red lines) with a 0.2 initial change in COVID19 life expectancy (blue line). If this population could sustain this change, its survival probability would increase without health deterioration for any further change in life expectancy. We found that for life expectancy, the distribution probability plot showed a 0.1–0.4 change in life expectancy (black lines), which would result in a major variation in death probability (blue lines). The modeled values varied from 0.1 to 0.9 on a log scale; they showed a maximum value for death probability of 135% on a linear scale [blue lines, [Figure 5]]. This finding shows that the initial response of body immunity is very important with older people following infection. Here, death probability was a log value in the magnitude scale; the death probability shift was slight; all Xaxis values were in log.  Figure 5: COVID19 death probability with change in COVID19 life expectancy for 65–70 aged populations
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With respect to smoking, we initialized the modeled value variations by considering 40%, 20%, and 30% uncertainty in the COVID19 death rate or COVID19 life expectancy, female smokers, and male smokers, respectively. Here, the red lines represent the designated value variation for the COVID19 death rate or COVID19 life expectancy; the blue lines indicate the modeled value variations.
At a 0.1 initial change in the COVID19 death rate (black lines), the COVID19 death probability was zero for smokers; for a 0.2–0.3 change in COVID19 death rate (black lines), the COVID19 death probability increased to 100% (red lines). The distribution probability plot indicated the range of changes in the death rate (0.3–0.4; black lines), resulting in a major change in death probability up to 100% (blue lines). If that change was sustained by smokers, their survival probability would increase that would indicate immunity development against COVID19 among smokers for further changes in the death rate. The modeled values (black lines) varied from 0.1 to 0.5 on a log scale; they showed a maximum value of death probability of 320% on a linear scale [blue lines, [Figure 6]]. Thus, we infer that smoking leads to increased mortality after COVID19 infection.  Figure 6: COVID19 death probability with change in COVID19 death rate for female–male smokers
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For a 0.1–0.3 (black lines) initial change in COVID19 life expectancy, the survival among smokers was 100% (blue lines). For a 0.3–0.8 initial change in COVID19 life expectancy (black lines), the COVID19 death probability was greater (blue lines). It reached a maximum of 80% (blue lines) for the values of 0.5–0.6 (black lines); thereafter, any change in COVID19 life expectancy or COVID19 death probability became zero for smokers as they developed immunity.
We found that for life expectancy, the distribution probability plot showed a major variation in death probability (blue lines) with a change in life expectancy of 0.5–0.6 (black lines). The modeled values varied from 0.2 to 1.1 (black lines) on a log scale, whereas they displayed a maximum value of death probability (100%) on a linear scale [blue lines, [Figure 7]]. This indicates that for smokers, the middle period (5–8 days) after infection was very important in terms of immunity.  Figure 7: COVID19 death probability with change in COVID19 life expectancy for female–male smokers
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Epidemiological Characteristic of COVID19   
We expressed the epidemiological characteristics of COVID19 among individuals aged 65–70 years and smokers in terms of the simulated CTSSM. High values for the first and second elements in the CTSSM indicate that COVID19 has a high sensitivity and death rate in the older population for the initial period (5 days) after infection; among smokers, that trend was evident in the middle period (5–8 days) after infection [Figure 8]. This finding indicates that the death rate was high and life expectancy low in that older population due to lowered immunity; in the case of smokers, it was because smoking had weakened the lungs and made them more vulnerable to infection.  Figure 8: Simulated epidemiological parameters of CTSSM, India. CTSSM = COVID19 transmission state space matrix
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Regarding the CTSSM, the average value of SD, kurtosis, mean, and skewness was, respectively, as follows: in A, 0.620, 2.810, 0.251, and 0.295; B, 0.624, 2.805, 0.246, and 0.293; C, 1.449, 2.639, 0.561, and 0.241; and D, 1.456, 2.636, 0.549, and 0.240. For the CTSSM parameters, the median SD was as follows: A, 0.098 (IQR, 0.001, 1.012); B, 0.101 (0.003, 1.017); C, 0.098 (0.001, 0.615); and D, 0.101 (0.096, 0.106). With the CTSSM parameters, the median kurtosis was as follows: A, 1.900 (IQR, 1.900, 3.748); B, 1.900 (1.900, 3.735); C, 1.900 (1.900, 2.794); and D, 1.900 (1.900, 2.785) [Table 1].  Table 1: Simulated epidemiological parameters of COVID19 Transmission State Space Matrix, India
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The area spread of death probability in individuals aged 65–70 years and among smokers appears in Supplementary [Figure 1] and [Figure 2] using CTSSM parameters by means of the knearest neighbor method. We found that the area spread of death probability in that older population was lower than that among smokers. The death probability among smokers was 1.905 times that of the older population (SI1).
Control Measures   
India adopted various measures to reduce COVID19 transmission. To assess the effectiveness of those measures, researchers have used the doubling rate, measured in days. However, the doubling rate is an ineffective tool in countries with a large infected population, such as the United States, India, Russia, and Brazil. In those cases, the growth of COVID19 cases is evaluated using the median growth rate (MGR), which measures growth in terms of the time (days) required for the number of infected cases to reach a value 1.5 times that of the previous number of COVID19 cases. In India, the MGR currently stands at 17 days.
The COVID19 measures adopted in India have produced good results, but they are insufficient: The country's infrastructure and workforce capabilities are good, but they were unable to halt the crisis. Doctors, nurses, and police officers became infected owing to shortages, such as personal protective equipment (Zhao et al. 2020). The present study has indicated some measures that could be adopted to help India tackle COVID19. The following are some of the measures that India should undertake: develop a sound scientific advisory body made up of field experts and researchers, not political representatives, to deal with such emergencies; use mathematical and statistical modeling to determine future COVID19 infection to rapidly provide additional resources to combat the pandemic; apply price freeze on household goods, such as food grains and milk; develop funds locally and nationwide (in Maharashtra); increase the doctortopatient ratio (Maharashtra); forbid home visits (Uttar Pradesh); ban the mass use of single toilets in slum areas (Maharashtra); ban access to malls and night clubs (Delhi); ban street vendors, roadside tea stalls, and weddings (Maharashtra); ban cafes and cultural, religious, business, and political events (nationwide) that result in mass gatherings; increase the budget for health, welfare, and safety (Bihar and West Bengal); develop good food distribution chains (Bihar, Andhra Pradesh, and Tamil Nadu); and encourage people to start physical fitness activities and eat healthy foods to improve their immune systems.
Acknowledgments
The authors are grateful for the experimental work support from the PVGs College of Engineering and Technology, Pune, India. All the numerical simulations were performed at the Computer Simulation Lab, Electrical Engineering Department, PVGs College of Engineering and Technology, Pune. The authors would like to thank Liwen Bianji (Edanz) (www. liwenbianji. cn/) for editing the English text of a draft of this manuscript.
Author contributions
P. G. Jamdade: Conceptualization, investigation, methodology, software, validation, writing – original draft, writing – review and editing.
S. G. Jamdade: Methodology, writing – review and editing.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
Supplementary Materials   
SI1: Area spread of death probability
Area spread is determined by using the knearest neighbor approach. Neurons (red dots) represent the positions of the 65–70 aged populations [Figure S1] of CTSSM. Neurons are linked each other using Euclidean distance of 1. Matrix representing 65–70 aged populations and COVID19 death rate is assigned as weight matrix while matrix representing 65–70 aged populations and COVID19 life expectancy was assigned as distance matrix.
On similar basis, area spread is determined using the knearest neighbor approach. Neurons (red dots) represent the positions of the female–male smokers [Figure S2] of CTSSM. Neurons are linked each other using Euclidean distance of 1. Matrix representing female–male smokers and COVID19 death rate is assigned as weight matrix while matrix representing female–male smokers and COVID19 life expectancy were assigned as distance matrix.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8]
[Table 1]
