A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population

In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common di...
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Gespeichert in:

Autor*in:	Kumar, Pushpendra [verfasserIn] Govindaraj, V. [verfasserIn] Erturk, Vedat Suat [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Teeth/tooth Cavity Mathematical model Caputo fractional derivative Existence and stability The predictor-corrector scheme

Übergeordnetes Werk:	Enthalten in: Chaos, solitons & fractals - Amsterdam [u.a.] : Elsevier Science, 1991, 161
Übergeordnetes Werk:	volume:161

DOI / URN:	10.1016/j.chaos.2022.112370

Katalog-ID:	ELV008230943

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520			\|a In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common disease in human teeth. As per our knowledge, to date, there is no mathematical model in the literature to understand the dynamics of the cavity. In this article, we fulfill this requirement by defining a non-linear delay-type mathematical model to describe the dynamics of cavities in human teeth. First, we propose an integer-order model and check the boundedness and positivity of the solution, and equilibrium points with their local and global asymptotically stability. After that, we generalize the integer-order delay-type model into a fractional sense to capture the memory effects. We prove the existence of a unique global solution of the fractional-order model in the Caputo derivative sense. The numerical solution of the proposed fractional-order model is given with the help of the predictor-corrector method. We do the all necessary graphical simulations to understand the model dynamics appropriately. The main motivation of this paper is to introduce a first mathematical delay-type model to describe the cavity problem in human teeth.
650		4	\|a Teeth/tooth
650		4	\|a Cavity
650		4	\|a Mathematical model
650		4	\|a Caputo fractional derivative
650		4	\|a Existence and stability
650		4	\|a The predictor-corrector scheme
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allfields	10.1016/j.chaos.2022.112370 doi (DE-627)ELV008230943 (ELSEVIER)S0960-0779(22)00580-X DE-627 ger DE-627 rda eng 510 DE-600 30.20 bkl 31.00 bkl Kumar, Pushpendra verfasserin aut A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common disease in human teeth. As per our knowledge, to date, there is no mathematical model in the literature to understand the dynamics of the cavity. In this article, we fulfill this requirement by defining a non-linear delay-type mathematical model to describe the dynamics of cavities in human teeth. First, we propose an integer-order model and check the boundedness and positivity of the solution, and equilibrium points with their local and global asymptotically stability. After that, we generalize the integer-order delay-type model into a fractional sense to capture the memory effects. We prove the existence of a unique global solution of the fractional-order model in the Caputo derivative sense. The numerical solution of the proposed fractional-order model is given with the help of the predictor-corrector method. We do the all necessary graphical simulations to understand the model dynamics appropriately. The main motivation of this paper is to introduce a first mathematical delay-type model to describe the cavity problem in human teeth. Teeth/tooth Cavity Mathematical model Caputo fractional derivative Existence and stability The predictor-corrector scheme Govindaraj, V. verfasserin aut Erturk, Vedat Suat verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 161 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:161 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 30.20 Nichtlineare Dynamik 31.00 Mathematik: Allgemeines AR 161
spelling	10.1016/j.chaos.2022.112370 doi (DE-627)ELV008230943 (ELSEVIER)S0960-0779(22)00580-X DE-627 ger DE-627 rda eng 510 DE-600 30.20 bkl 31.00 bkl Kumar, Pushpendra verfasserin aut A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common disease in human teeth. As per our knowledge, to date, there is no mathematical model in the literature to understand the dynamics of the cavity. In this article, we fulfill this requirement by defining a non-linear delay-type mathematical model to describe the dynamics of cavities in human teeth. First, we propose an integer-order model and check the boundedness and positivity of the solution, and equilibrium points with their local and global asymptotically stability. After that, we generalize the integer-order delay-type model into a fractional sense to capture the memory effects. We prove the existence of a unique global solution of the fractional-order model in the Caputo derivative sense. The numerical solution of the proposed fractional-order model is given with the help of the predictor-corrector method. We do the all necessary graphical simulations to understand the model dynamics appropriately. The main motivation of this paper is to introduce a first mathematical delay-type model to describe the cavity problem in human teeth. Teeth/tooth Cavity Mathematical model Caputo fractional derivative Existence and stability The predictor-corrector scheme Govindaraj, V. verfasserin aut Erturk, Vedat Suat verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 161 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:161 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 30.20 Nichtlineare Dynamik 31.00 Mathematik: Allgemeines AR 161
allfields_unstemmed	10.1016/j.chaos.2022.112370 doi (DE-627)ELV008230943 (ELSEVIER)S0960-0779(22)00580-X DE-627 ger DE-627 rda eng 510 DE-600 30.20 bkl 31.00 bkl Kumar, Pushpendra verfasserin aut A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common disease in human teeth. As per our knowledge, to date, there is no mathematical model in the literature to understand the dynamics of the cavity. In this article, we fulfill this requirement by defining a non-linear delay-type mathematical model to describe the dynamics of cavities in human teeth. First, we propose an integer-order model and check the boundedness and positivity of the solution, and equilibrium points with their local and global asymptotically stability. After that, we generalize the integer-order delay-type model into a fractional sense to capture the memory effects. We prove the existence of a unique global solution of the fractional-order model in the Caputo derivative sense. The numerical solution of the proposed fractional-order model is given with the help of the predictor-corrector method. We do the all necessary graphical simulations to understand the model dynamics appropriately. The main motivation of this paper is to introduce a first mathematical delay-type model to describe the cavity problem in human teeth. Teeth/tooth Cavity Mathematical model Caputo fractional derivative Existence and stability The predictor-corrector scheme Govindaraj, V. verfasserin aut Erturk, Vedat Suat verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 161 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:161 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 30.20 Nichtlineare Dynamik 31.00 Mathematik: Allgemeines AR 161
allfieldsGer	10.1016/j.chaos.2022.112370 doi (DE-627)ELV008230943 (ELSEVIER)S0960-0779(22)00580-X DE-627 ger DE-627 rda eng 510 DE-600 30.20 bkl 31.00 bkl Kumar, Pushpendra verfasserin aut A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common disease in human teeth. As per our knowledge, to date, there is no mathematical model in the literature to understand the dynamics of the cavity. In this article, we fulfill this requirement by defining a non-linear delay-type mathematical model to describe the dynamics of cavities in human teeth. First, we propose an integer-order model and check the boundedness and positivity of the solution, and equilibrium points with their local and global asymptotically stability. After that, we generalize the integer-order delay-type model into a fractional sense to capture the memory effects. We prove the existence of a unique global solution of the fractional-order model in the Caputo derivative sense. The numerical solution of the proposed fractional-order model is given with the help of the predictor-corrector method. We do the all necessary graphical simulations to understand the model dynamics appropriately. The main motivation of this paper is to introduce a first mathematical delay-type model to describe the cavity problem in human teeth. Teeth/tooth Cavity Mathematical model Caputo fractional derivative Existence and stability The predictor-corrector scheme Govindaraj, V. verfasserin aut Erturk, Vedat Suat verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 161 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:161 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 30.20 Nichtlineare Dynamik 31.00 Mathematik: Allgemeines AR 161
allfieldsSound	10.1016/j.chaos.2022.112370 doi (DE-627)ELV008230943 (ELSEVIER)S0960-0779(22)00580-X DE-627 ger DE-627 rda eng 510 DE-600 30.20 bkl 31.00 bkl Kumar, Pushpendra verfasserin aut A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common disease in human teeth. As per our knowledge, to date, there is no mathematical model in the literature to understand the dynamics of the cavity. In this article, we fulfill this requirement by defining a non-linear delay-type mathematical model to describe the dynamics of cavities in human teeth. First, we propose an integer-order model and check the boundedness and positivity of the solution, and equilibrium points with their local and global asymptotically stability. After that, we generalize the integer-order delay-type model into a fractional sense to capture the memory effects. We prove the existence of a unique global solution of the fractional-order model in the Caputo derivative sense. The numerical solution of the proposed fractional-order model is given with the help of the predictor-corrector method. We do the all necessary graphical simulations to understand the model dynamics appropriately. The main motivation of this paper is to introduce a first mathematical delay-type model to describe the cavity problem in human teeth. Teeth/tooth Cavity Mathematical model Caputo fractional derivative Existence and stability The predictor-corrector scheme Govindaraj, V. verfasserin aut Erturk, Vedat Suat verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 161 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:161 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 30.20 Nichtlineare Dynamik 31.00 Mathematik: Allgemeines AR 161
language	English
source	Enthalten in Chaos, solitons & fractals 161 volume:161
sourceStr	Enthalten in Chaos, solitons & fractals 161 volume:161
format_phy_str_mv	Article
bklname	Nichtlineare Dynamik Mathematik: Allgemeines
institution	findex.gbv.de
topic_facet	Teeth/tooth Cavity Mathematical model Caputo fractional derivative Existence and stability The predictor-corrector scheme
dewey-raw	510
isfreeaccess_bool	false
container_title	Chaos, solitons & fractals
authorswithroles_txt_mv	Kumar, Pushpendra @@aut@@ Govindaraj, V. @@aut@@ Erturk, Vedat Suat @@aut@@
publishDateDaySort_date	2022-01-01T00:00:00Z
hierarchy_top_id	314118497
dewey-sort	3510
id	ELV008230943
language_de	englisch
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author	Kumar, Pushpendra
spellingShingle	Kumar, Pushpendra ddc 510 bkl 30.20 bkl 31.00 misc Teeth/tooth misc Cavity misc Mathematical model misc Caputo fractional derivative misc Existence and stability misc The predictor-corrector scheme A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population
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topic_title	510 DE-600 30.20 bkl 31.00 bkl A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population Teeth/tooth Cavity Mathematical model Caputo fractional derivative Existence and stability The predictor-corrector scheme
topic	ddc 510 bkl 30.20 bkl 31.00 misc Teeth/tooth misc Cavity misc Mathematical model misc Caputo fractional derivative misc Existence and stability misc The predictor-corrector scheme
topic_unstemmed	ddc 510 bkl 30.20 bkl 31.00 misc Teeth/tooth misc Cavity misc Mathematical model misc Caputo fractional derivative misc Existence and stability misc The predictor-corrector scheme
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title	A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population
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title_full	A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population
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title_sort	a novel mathematical model to describe the transmission dynamics of tooth cavity in the human population
title_auth	A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population
abstract	In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common disease in human teeth. As per our knowledge, to date, there is no mathematical model in the literature to understand the dynamics of the cavity. In this article, we fulfill this requirement by defining a non-linear delay-type mathematical model to describe the dynamics of cavities in human teeth. First, we propose an integer-order model and check the boundedness and positivity of the solution, and equilibrium points with their local and global asymptotically stability. After that, we generalize the integer-order delay-type model into a fractional sense to capture the memory effects. We prove the existence of a unique global solution of the fractional-order model in the Caputo derivative sense. The numerical solution of the proposed fractional-order model is given with the help of the predictor-corrector method. We do the all necessary graphical simulations to understand the model dynamics appropriately. The main motivation of this paper is to introduce a first mathematical delay-type model to describe the cavity problem in human teeth.
abstractGer	In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common disease in human teeth. As per our knowledge, to date, there is no mathematical model in the literature to understand the dynamics of the cavity. In this article, we fulfill this requirement by defining a non-linear delay-type mathematical model to describe the dynamics of cavities in human teeth. First, we propose an integer-order model and check the boundedness and positivity of the solution, and equilibrium points with their local and global asymptotically stability. After that, we generalize the integer-order delay-type model into a fractional sense to capture the memory effects. We prove the existence of a unique global solution of the fractional-order model in the Caputo derivative sense. The numerical solution of the proposed fractional-order model is given with the help of the predictor-corrector method. We do the all necessary graphical simulations to understand the model dynamics appropriately. The main motivation of this paper is to introduce a first mathematical delay-type model to describe the cavity problem in human teeth.
abstract_unstemmed	In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common disease in human teeth. As per our knowledge, to date, there is no mathematical model in the literature to understand the dynamics of the cavity. In this article, we fulfill this requirement by defining a non-linear delay-type mathematical model to describe the dynamics of cavities in human teeth. First, we propose an integer-order model and check the boundedness and positivity of the solution, and equilibrium points with their local and global asymptotically stability. After that, we generalize the integer-order delay-type model into a fractional sense to capture the memory effects. We prove the existence of a unique global solution of the fractional-order model in the Caputo derivative sense. The numerical solution of the proposed fractional-order model is given with the help of the predictor-corrector method. We do the all necessary graphical simulations to understand the model dynamics appropriately. The main motivation of this paper is to introduce a first mathematical delay-type model to describe the cavity problem in human teeth.
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title_short	A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population
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author2	Govindaraj, V. Erturk, Vedat Suat
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up_date	2024-07-06T18:59:30.394Z
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A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population

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