Mathematical Modelling of the Relationship between Two Different Temperament Classifications: During the Covid-19 Pandemic

In medicine, it is well known that healthy individuals have different physical and mental characteristics. Ancient Indian medicine, Ayurveda and the Persian-Arabic traditional Unani medicine has two distinct approaches for the classification of human subjects according to their temperaments. The individual temperament is an important foundation for personalized medicine, which can help in the prevention and treatment of many diseases including COVID-19. This paper attempts to explore the relationship of the utmost important concepts of these systems called individual temperament named as Prakruti in Ayurveda and Mizaj in Unani practice using mathematical modelling. The results of mathematical modelling can be adopted expediently for the development of algorithms that can be applied in medical informatics. For this, a significant literature review has been carried out. Based on the previous researchers' reviews the essential parameters have been identified for making the relationship and hypothesis were framed. The mathematical modelling was adopted to propose the existence of the relationship between the parameters of such an ancient and rich medicine systems. The hypotheses are validated through the mathematic driven model.

Nepal, Sri-Lanka, etc. It is also becoming popular in western countries including United States. Unani Tibbs is practiced mostly in India, Pakistan, Bangladesh, Iran, etc. It is also practiced in South Africa and United Kingdom.
There is a need of comparing this ancient wisdom of south Asia, to derive the best of both systems. However, there exist many barriers to this issue. Most of the research and authentic texts of Ayurveda are in Sanskrit or Hindi while for Unani, it is in Arabic, Persian or Urdu. A less amount of authentic literature is available in English. Many of times physician are not ready to cooperate with each other's. This integration and comparison will not only help in treatment and prevention of dieses but also promotion of healthy lifestyle.
In this paper, we have tried to compare and co-related one of important concept of these system called individual temperament, known as Prakruti/Prakriti in Ayurveda and Mizaj in Unani practice. We have used mathematical modelling to prove the existence of relationship between these twin temperaments. Although a lot of clinical trials and authenticated research will be required in future for validation of the concept. The outcome of this study could play an imperative role in providing support in bringing the concept into applied system using ICT. In addition, this paper can also contribute to the body of knowledge by acting as foundation stone in this step.

2-Literature Review
The previous literatures have been reviewed in order to find out and compare the applications of temperaments studies in treatment and immunology, the historical and modern development in the field of Ayurveda as well Unani medicine.

2-1-Ayurvedic Temperament (Prakruti)
According to Ayurveda every individual as specific temperament (Prakruti/Prakriti), which can be understood as mind-body constitutions. This temperament is based on Dosha, which are Vata, Pitta and Kappa. The health of an individual is influenced by their innate proportion of these three Dosha and their current state of balance or Vikruti (disequilibrium) [1]. Vata, Pitta and Kappa are the three Dosha assumed to be present in the human body, and their imbalance is the major cause of state of health. Treatments always aim at restoring the balance. The dominance of any Dosha in a person determines his or her Temperament, at the gross level [2]. The Doshas, continuously formed in the human body are responsible for the homeostasis and metabolic activities of an individual. The proportion of Doshas constituents is unique for every person and is termed as his/her Temperament. Temperament determines the physiological and psychological tendencies and influences their physiological features like the texture and color of the skin, hair, eyes, length of fingers, the shape of the palm, body frame, strength of digestion etc., and psychological features like their nature (introverted, extroverted, calm, excitable, intense, laid-back), including their reaction to stress. Generally, Temperament does not change throughout the lifetime of a person and can be used to access the patient's suitability for a treatment [3].
Dosha Prakruti can be determined scientifically using Physical, Physiological and Psychological Characters [4]. The Ayurvedic physician use various means for temperament assessment. This will include like physical examination, involving visual, tactile, olfactory, and auditory assessments; inference based on information collected, by indirect means including asking questions does the traditional method of Ayurvedic temperament determination and conclusions drawn based on available data, knowledge, and experience [5]. These methods can be broadly Touch based, Question based, or observation based [6].
For Temperament assessment Ayurveda practitioners sometime chooses a self-reported or structured interview constitutional questionnaire; however, is no standardized or validated self-reported constitutional questionnaire tool employed by physicians or institutions. There are a variety of questionnaires, publicly available, which are developed by either developed by researchers, educational institutions and Ayurveda products companies [7]. Different researchers have developed different questionnaire or observation tables based on ancient texts. Bell et al. used 10 question based on physiological or psychological characteristic e with 3 options representing each Dosha to select from [1]. Similarly, 31 physiological and psychological characteristics observed by Ayurvedic doctors can be found in Kshirsagar and Magno (2011) [8]. Usha and Vasant (2005), Prasher et al. (2008) developed a lengthy questionnaire with for clinical phenotyping was designed based on Ayurvedic literature on phenotypes and methods of Prakriti assessment [9][10]. Sixteen physical features were studied to assess Ayurvedic temperament according to the classical textual references in Ayurveda by Jyothy and Siddhali (2017) [11]. There have been several attempts at designing the reliable tools and protocols for assessment of temperament which each suffers from its own limitations [12].

2-2-Unani Temperament (Mizaj)
According to Unani postulates, there are four major fluids in a human body, i.e., four independent parameters which determine the health status of an individual. These are named Balgham (phlegm), dam (blood), Safra (yellow bile), and Sauda (black bile) respectively. When these fluids are present in the right proportion in the body, the body remains healthy. Based on dominance of anyone of the humors the Temperament of a person is determined [13]. The human temperaments corresponding to these fluids are, respectively, sanguine (Damvi), phlegmatic (Balghami), choleric (Safrawi) and melancholic (Saudawi). Each person is considered to have a specific humoral makeup, determined by the predominance of a given fluids in his or her constitution. The quality and quantity of the fluids in person's unique, determines and guarantee healthy conditions, while misbalance may result in ailment or disease [14]. Temperament (temperament) which is an important concept of Unani medicine, represents the metabolic constitution, psychological makeup and behavioral pattern of an individual [15].
Unani physicians have described several parameters for determination of Temperament. The most acceptable and appropriate determinants have been given by Ibn-e-Sina (980-1037 AD) in his famous book Al-Qanoon-fil-Tibb., he suggested 10 parameters for the assessment of Temperament such as physique, physiology, psychology, responsiveness of organs, etc. [16]. Hakim Sayed (1980) has developed a tool with 55 sub parameters of these from 10 classes [17]. Some other text has used around questionnaire with 20 sub parameters based on these 10-class developed from classical texts [18]. According to Akhtari (2018) there is absence of a homogenous method for evaluating temperament [19]. Most of the researcher in India use a standard questionnaire formulated by Central Council for Research in Unani Medicine (CCRUM), Ministry of AYUSH, New Delhi for assessment Temperament (temperament) of the subjects [18]. Mojahed et al. (2014) tried to study self-administered Temperament questionnaire for assessing its reliability and validity in Iran. The researchers found that most of the questionnaire based on classic literature's Temperament identification indices had satisfactory reliability. The authors suggested development of a brief self-report Temperament estimating [20]. Mozaffarpur et al. (2017) tried to investigate agreement between personal medicine experts in Temperament identification and to categorize the criteria used for Temperament identification. The researchers found that till that time there was no standard protocol for Temperament assessment. Each expert in their study participated in the project using their own method to determine Temperament. There researcher felt a strong need for increasing the agreement between experts in designing and validating standard scales for determination of Temperament [21]. Roshandel et al. (2016) tried to prepare a standard questionnaire on assessment of Temperament using classical texts in Greek, Arabic, and Persian. The questionnaire, however, need to be further tested and validated [22]. Bhushan et al. (2005) found a co-relation between Dosha prakruti and genotypes, the researchers found observed a reasonable correlation between HLA type and Prakriti type [23]. Rotti et al. (2014) studied relationship between temperament and immunology, they found the exisance relationship between immune response and individual temperament, which is in conformity with textual references in Ayurveda [24]. Relationship of temperament and cancer has been studied by Venkataraghavan et al. (1987) [25]. Similarly, Joob and Viroj (2012) studied the relationship between Temperament and diabetes [26]. In the current period, the importance of Temperament in dealing with COVID 19 were studied by Nair  Setooni et al. (2016) found that physical activity and sedentary behavior is affected by individual Unani Temperament [30]. , studied the relationship of Temperament with immunity [31]. The relationship between cancer type and humoral temperament was studied by Carden and Judson (2008) [32]. IIkhani et al. (2019), Baig et al. (2018) studied relationship between Temperament and diabetes [33][34]. In the current epoch, the importance of Temperament in dealing with COVID 19 were studied by Nikhat and Fazil (2020),   [35][36].

2-4-Use of Modern Scientific Tools in Assessment of Ayurveda and Unani Temperaments
Some researchers have used various modern scientific tools for automatic assessment and analysis of temperament like Pulse diagnosis [37][38]. Khajuria (2020) used the software to detect the body pain using classification prototype [39]. Wedaduru is Ayurveda based decision support system developed in Srilanka for disease screening and remedy analysis solution [40], similarly Ayusoft is a the Indian decision support system for Ayurveda, developed with a vision to convert classical Ayurvedic texts into comprehensive, authentic, intelligent and interactive knowledge repository with complex analytical tools. Prakriti assessment by Ayusoft works using weightage configuration [41,5]. A mobile device application was designed to enables an Ayurvedic clinician to enter and share a patient's Dhosa by Stranieri et al. [42].  [43][44][45]. Similarly, researchers applied Neural networks [46], computer vision [3], using anthropometric parameter [47][48][49].
Some of the researchers have tried to relate scientifically Unani temperament with somatotypes [50][51]. Nasir (2019) used computerized image processing to the assess the color and shape of the individual's hair. The thickness of hair was measured by the Digital Vernier Caliper. This data was used in accessing Unani temperament [52]. Afrough and Forooque (2012) suggested integration of Unani temperament assessment tool with data mining capability in hospital management system [53].

2-5-Mapping of Ayurvedic and Unani Temperaments
Mulla et al. (2014) compared the system using questionnaires [58]. Mulla et al. (2013) used artificial neural networks to get Unani Temperament from Ayurvedic Temperament and vise-versa. Some researchers both ancient and modern who have tried to solve the problem of mapping the two [59]. Rolfe (2002) has suggested in the relationship between three Ayurvedic Dosha and four Unani Temperament can be mapped. She presented Balgham and Sauda together, as kappa, dam is Vata, Safra as pitta [60]. Endo and Nakamura (1995) proposed that Blood i.e. Dam to be considered as the combinations of all other three Doshas [61]. Guha quoted Maharishi Sushruta, who has included blood or Dam or Shonit as the main constituent together along with other three Doshas [62].
There exist very few literatures comparing both the system, there is still a wide gap. There is a strong need to bridge this gap. Although from above literatures, we found that there is no consensus among the scholars regarding the mapping of these two temperaments. We proposed to use the mathematical modeling to deduce the relationship between these two temperaments of an individual.

3-Theory of Equivalence of Two Classification Methods
Let us consider there is a set X of n objects = { 1 , 2 , 3 … , }.. There can be different methods of classification or grouping of these objects, let us consider that there are two methods i.e., m1 and m2. The first method (m1) classifies objects in three groups A, B, C, using attributes independently measured according to one method of 'information generation'.
Let us consider there is a set of n objects = { 1 , 2 , 3 … , }. There can be different methods of classification or grouping of these objects, let us consider that there are two methods i.e., 1 and 1 .
The first method 1 classifies objects in three groups A, B, C, using attributes independently measured according to one method of 'information generation'. The second method 2 classifies objects into four groups i.e. , , , , using attributes independently measured according to second method of 'information generation'. However, the attributes talk about the same final 'information', which is the hidden real class of object so our fist axiom is that: Mathematically speaking (equation 1) is a three-parameter system where as (Equation 2) is a four-parameter system. It is a well-known fact that in the presence of a relation of the type = ( , , ), if it exists (Equation 2) would also reduce to a three-parameter system with a natural mapping between the two systems as: In other words, each P, Q, R, is a proper mix of A, B, C and S is a combination of P, Q, and R, hence is indirectly dependent on A, B, C. Though (equation 3) projects the relationship as linear, in reality linearity is not mandatory.

What can be the relationship between ABC and PQRS?
 A= P, B= Q, C=R and S = AB and so on there will be infinitely many options.
 A=P, B=Q, C= R, ABC=S can be an alternative  A=PQR, B=QRS, C=PQRS

4-Mathematical Deduction
Ayurvedic and Unani Temperament are the two methods of classification human subjects according to their temperaments. Let us find mathematically deduce relationship between these two methods ( 1 and 2 ). According to the theory of Ayurveda every individual ( ) has (Equation 3) Dosha i.e., Vata, Pitta, & Kappa denoted by: For every there is a unique combination of , , every individual will have a degree of membership in all three Dosha and no Dosha is absent therefore we say that the degree of membership is fuzzy: The Ayurvedic Temperament of an individual can be determined based on dominance of the Dosha. No two Dosha will be equal in any case. The most dominant Dosha will be the temperament of the individual. i.e., Ayurvedic temperament ( ) can be determined as: ω, π and k can have any values between 0 and 1.0. Every individual ( ) has degree of membership of all three sets, i.e. ω, π & k the maximum belonging will be determined by maximum membership. If there is any change in the value of ω, π or k the temperament is distort to ′, there is condition of instability and health is distorted and it should be brought back to the stable condition. Similarly, according to theory of Unani Tibb, every Individual ( ) has four fluids i.e. Balgham, Dam, Sauda, Safra denoted by = { , , , ∅ } For every there is a unique combination of , , ∅ , every individual will have a degree of membership in all four fluids and no fluid is absent therefore we say that the degree of membership is fuzzy: The Unani Temperament of an individual can be determined based on dominance any one of these fluids i.e. Unani temperament.
can be determined as: = max ( , , , ∅) Every individual has degree of membership of all four sets, i.e. , , ∅ the maximum belonging determines the maximum membership. If there is change in value of any , , ∅ the temperament is distorted to '. It has to be brought again back to normal .
Relationship: as per the Equation 5 and 8, we can say that: When changes to ′ and changes to '. Based on the above statement we framed the following hypotheses: H1: ( , , ∅) obtained by UNANI method of investigation can predict ( , , ) of Ayurvedic investigation.

5-Results and Discussion
Let us summarize the research that have compared both methods. R. Rolfe (2002) has suggested in the relationship between ayurvedic Dosha and Unani humors/temperaments, which can mathematically state as follows [60]: It was proposed that Blood i.e., Dam was comprised of the properties of every humor without having its own peculiar properties [61]. Therefore, the diseases caused by deranged "blood" were regarded as an aggregate disease caused by the other three deranged humors. This is stated as follows: Guha of Banaras Hindu University stressed that , , ∅ of Unani system can be compared with , , respectively. In Tridosha theory has not been included but Maharishi Sushruta has enumerated Shonit ( ) as the main constituent together with Tridosha [62]. This is stated as: Unani values for , , , ∅ and Ayurvedic values for , , the healthy individuals of both genders was obtained in an experiment by [59]. The ANN Model was developed using a data set of 73% of the records and was tested with 27% of the records. The weights of hidden layer were calculated using multiple regressions. We proposed a model of relationship based on the findings of [59], which is expressed: respectively. The is a vector of three components as indicated above. We propose U2A Model which takes as input and gives as output with reasonable accuracy. i.e.; Similarly, the can we have a reverse model, Where 1 and 2 are a random error factor.
Naisal and Kumar (2016) has adopted Sostak Fuzzy Topology to mathematically represented the Ayurveda temperament [63], similarly Smarandache, (2018) adopted nuetropsychic logic to represent the Unani temperament [64], but none of the scholars of mathematics have compared both or tried to mutually convert from one system from another.
In the present study, the researchers have established that it is mathematically possible obtain Ayurvedic temperament of an individual, if the unani temperament is known and vice versa. As evident from the Equations 14 and 15. Previous research although (Endo and Nakamura (1995)

6-Conclusion
The Present research is multi-disciplinary in method, where two different ancient medical systems are equated using mathematical approach, which can be used in development of Information system. Traditional and alternative medicine give more Importance to individual difference while treating a person. This evident from the methodology adopted in Ayurveda and Unani medical approaches. The Ayurvedic temperament, which is three-parameter system, while Unani temperament e is a four-parameter system. Both of this system represent same truth in different perspective. Hence, it can be believed that there must be some relationship between these two representations. It should be possible to obtain value of one from another. To establish any fact or concept it should be first established using formal theory and later empirically validated. In order to establish the formal theory, mathematical modelling was to obtain Ayurvedic temperament from Unani (A2U) and Unani temperament from Ayurveda (U2A). The result indicates, it is mathematical possible to obtained one from another with some amount of error, if this error is minor, then it is a great achievement. However, there is a need lot of trials, experimentations, and validating the concept with actual data. If it is successful then it can give benefit of both systems, especially in case dealing with those medical and health issue which stressed more on the individual differences and personalized medicine including COVID-19 etc. Once it is established and empirically validated, it can be used in development of health care information system. This information system would be a blend of modern medicine, backed back by ancient wisdom of health and immunity, implemented using neural network, fuzzy logic, deep learning, machine learning etc. algorithm with robust Information Technology infrastructure.

7-1-Author Contributions
The article is joint interdisciplinary contribution of four different authors, the first author M.A.A.R. made the study conception and design, second and corresponding Author M.M.J.F. has done review of the literature for the research.
The Third Author H.S.A., who is from area of mathematics validated, and improved the developed mathematical model. The fourth author M.S.A.Q. is from the field of medical science. He reviewed and validated the paper from medical science perspective. All authors reviewed the results and approved the final version of the manuscript.

7-2-Data Availability Statement
No new data were created or analyzed in this study. Data sharing is not applicable to this article.

7-3-Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.

7-4-Acknowledgements
The authors would like to acknowledge the researcher G. Mulla, M. J. M. Farooque and H. S. Acharya, for providing us the data of ANN model. The authors would also acknowledge Dhofar University Oman, Pune University India, Almaarefa University KSA.

7-5-Conflicts of Interest
The author declares that there is no conflict of interests regarding the publication of this manuscript. In addition, the ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancies have been completely observed by the authors.