Mathematical Biology
Address: Dr.Kalyan Das
Professor and Dean (SW)
National Institute of Food Technology Entrepreneurship and Management(Govt. of India)
Department of Mathematics, Plot No. 97, Sector 56, HSIIDC Industrial Estate,Kundli - 131028, Haryana, India.
E-mail: [email protected] / [email protected]
Address: Dr.Kalyan Das
Professor and Dean (SW)
National Institute of Food Technology Entrepreneurship and Management(Govt. of India)
Department of Mathematics, Plot No. 97, Sector 56, HSIIDC Industrial Estate,Kundli - 131028, Haryana, India.
E-mail: [email protected] / [email protected]
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model system, it is shown that there exists an optimal control of the virus replication rate. The characterization of the optimal control is explained as well. The optimality of the viral cytotoxicity is also studied. Numerical simulations are presented to validate the analytical findings. Finally, we conclude some epidemiological remarks made through analytical and numerical observations.
system. A case study is presented to investigate the impact of the pH content in the eutrophication of aquatic hyacinths. To understand the interaction of aquatic species, we propose a mathematical model by considering the components of aquatic reserve structure in a maritime condition that involves two locales: aquatic hyacinth region and aquatic hyacinth liberated region. The model depicts a quantitative correlation between aquatic hyacinth and aquatic biomass. We analyze the stability of the steady states, which can help to understand the persistence and extinction of the species in the two regions mentioned above. Numerical simulation is carried out to conceive the distribution of aquatic species in two aquatic hyacinth regions. Furthermore, we impose white noise in the model to address the environmental heterogeneity of aquatic structures and subsequently inspect their influences on the inhabitants of the aquatic hyacinth region and aquatic hyacinth liberated region.
A sensitivity analysis of the parameters is performed to identify the dominant parameters in the model. The analysis shows that numerical investigations comply with the stochasticity analysis of the system. Numerical results reveal that the amplitude of oscillations of the species of aquatic hyacinth region is higher than that of the aquatic hyacinth liberated region for any choice of the white noises, which has a reasonable agreement with the real aquatic biomass.
polymeric or nonpolymeric materials like cellulose, ethylene glycol, and gelatin. There are several techniques used for microencapsulation. Fluidized bed coating, spray cooling, spray drying, extrusion, and coacervation are few to be named. The selection of a particular technique depends upon the properties of the core material, encapsulant,
and different properties and morphology of the capsules desired. The characterization and optimization of efficient and successful encapsulation can be done by studying the encapsulation efficiency and various properties of the capsules like morphology, size, hydrophobicity, hygroscopicity, solubility, surface tension, thermal behavior, and
mechanical properties. Microencapsulation is a technology that is extensively used in foods, whether as a fortifying tool or as a mode for the development of a functional food. Based on the fundamental understanding of encapsulation and latest research and findings from literature, this review critically analyses and brings together the utilization of this particular technique in foods, different methods used for encapsulation, different properties of the capsules which result from the different techniques adopted for microencapsulation and different release mechanisms used for delivering the compounds.
number of the SQIRP system is designed using the next cohort matrix process. The SQIRP system has asymptotically stable
locally at an infection-free equilibrium point when the basic reproduction
number is not more than unity and unsteady when the value
is greater than unity. The SQIRP system is found to go through a
backward bifurcation, which is a novel perspective for Coronavirus
infection transmission. The infection-free equilibrium and endemic
equilibrium are shown to be asymptotically stable globally using the
Lyapunov function hypothesis and the invariance principle of Lasalle.
A SQIRP system with backward bifurcation is explored using stochastic
analysis. The ecological stochasticity in the appearance of white
noise best describes the system’s value. To verify the results, more
numerical simulations are run.
to the modeling of interacting species in which prey has nonlinear repro-
duction, which is in competition with predator. The mathematical model's
stochastic stability is investigated. The method of designing appropriate
Lyapunov functions is used to identify permanence conditions among the
parameters of the model and conditions for the structure to no longer be
extinct. The system's two-dimensional di usive stability is regarded and
studied. The system experiences the process of saddle-node bifurcation
by varying the death rate of predator parameter. Further e ects of pa-
rameters that undergo inherent oscillations are numerically investigated,
revealing that as the intensity of predation parameter b is increased, the
device encounters non-periodic and damped oscillations.
proposed model in view of stability of the system with appropriate chosen attributes. Our findings are more focused on nanoparticle-induced aquatic ecosystem which may stabilize or destabilize the system, resulting in sensitive analysis through various parametric values. Furthermore, the depletion of nanoparticles from the aquatic system plays an important role for the steady coexistence of the host and commensal organisms, as contact rates between nanoparticles and hosts increase. Finally, the analytical results are verified and exposed through computer simulations which are quite interesting.
basic reproduction numbers. Hopf bifurcation is detected in the system, and a time delay is inserted in the transmission terms to represent the virus's incubation period. The spread of the novel COVID-19 strain to
humans is influenced by environmental conditions such as mugginess, precipitation, and temperature. To explore the impact of environmental oscillations on the coronavirus, we employ white noise perturbations in
the system. Finally, we examine the mathematical reenactments using MATLAB.
steadiness are indomitable. Finally, an ideal collecting strategy is conversed by applying Pontryagin’s maximal principle. It also addresses the steadiness of framework through mathematical reproduction utilizing MATLAB.
1993, followed by that in 1997; whereas it was a minimum in the year 1980, with an extension in its frequency in the subsequent years 1981 and 1982. The coefficient of variation of both annual and seasonal thunderstorm days is minimum over the areas of maximum frequency of mean thunderstorm days and vice-versa. The time-domain analysis confirms that the occurrence happened to be maximum in the year 1991, although each and every state did not witness thunderstorms every year. Also some other time-domain models like autocorrelation and seasonal integrated moving average provide adequate evidence for exploring the number of thunderstorms which happen to confirm the trend of
occurrence of thunderstorm over the years.
equations involving volatile compounds and microbial populations separately. TVB-N and TVC of stored rohu fish was determined at an interval of 4 days for 24 days. The initial and final biomass of TVB-N was 4.57 (fresh sample), 19.88 (24 days at 5◦C), and 7.10 mg/100 g (24th day at 0◦C), respectively. The TVC values were found to be 2.29 (fresh
sample), 9.5 (24 days at 5◦C) and 8.1 log (cfu/g) (24 days at 0◦C). Exponential, modified exponential, Howgate, and adapted Howgate models were considered for modeling the TVB-N formation, whereas logistic, modified logistic, Gompertz, and modified Gompertz
model were taken forward for modeling the microbial biomass developed in stored rohu fish. The exponential model found be the best fit model fit model for TVB-N prediction in rohu fish stored at 0 and 5◦C as it showed the highest R2 (0.9796, 0.9887) the lowest chi square
2 (0.2782, 0.3976), RMSE (0.52741, 0.6306) AIC (−7.3122, −4.8106), AICc (−0.5122, 1.9894) and BIC (−7.4204, −4.9188), respectively. The Gompertz model was found to be the best fit model for microbial biomass prediction in rohu fish stored at 5◦C (R2 = 0.9947, chi square
2 = 0.0537, AIC = −18.379, AICc = −6.3792 and BIC = −18.542), in
contrast, both of the logistic and modified logistic models were the best suited at 0◦C storage condition (R2 = 0.9919, chi square = 0.0823).
model system, it is shown that there exists an optimal control of the virus replication rate. The characterization of the optimal control is explained as well. The optimality of the viral cytotoxicity is also studied. Numerical simulations are presented to validate the analytical findings. Finally, we conclude some epidemiological remarks made through analytical and numerical observations.
system. A case study is presented to investigate the impact of the pH content in the eutrophication of aquatic hyacinths. To understand the interaction of aquatic species, we propose a mathematical model by considering the components of aquatic reserve structure in a maritime condition that involves two locales: aquatic hyacinth region and aquatic hyacinth liberated region. The model depicts a quantitative correlation between aquatic hyacinth and aquatic biomass. We analyze the stability of the steady states, which can help to understand the persistence and extinction of the species in the two regions mentioned above. Numerical simulation is carried out to conceive the distribution of aquatic species in two aquatic hyacinth regions. Furthermore, we impose white noise in the model to address the environmental heterogeneity of aquatic structures and subsequently inspect their influences on the inhabitants of the aquatic hyacinth region and aquatic hyacinth liberated region.
A sensitivity analysis of the parameters is performed to identify the dominant parameters in the model. The analysis shows that numerical investigations comply with the stochasticity analysis of the system. Numerical results reveal that the amplitude of oscillations of the species of aquatic hyacinth region is higher than that of the aquatic hyacinth liberated region for any choice of the white noises, which has a reasonable agreement with the real aquatic biomass.
polymeric or nonpolymeric materials like cellulose, ethylene glycol, and gelatin. There are several techniques used for microencapsulation. Fluidized bed coating, spray cooling, spray drying, extrusion, and coacervation are few to be named. The selection of a particular technique depends upon the properties of the core material, encapsulant,
and different properties and morphology of the capsules desired. The characterization and optimization of efficient and successful encapsulation can be done by studying the encapsulation efficiency and various properties of the capsules like morphology, size, hydrophobicity, hygroscopicity, solubility, surface tension, thermal behavior, and
mechanical properties. Microencapsulation is a technology that is extensively used in foods, whether as a fortifying tool or as a mode for the development of a functional food. Based on the fundamental understanding of encapsulation and latest research and findings from literature, this review critically analyses and brings together the utilization of this particular technique in foods, different methods used for encapsulation, different properties of the capsules which result from the different techniques adopted for microencapsulation and different release mechanisms used for delivering the compounds.
number of the SQIRP system is designed using the next cohort matrix process. The SQIRP system has asymptotically stable
locally at an infection-free equilibrium point when the basic reproduction
number is not more than unity and unsteady when the value
is greater than unity. The SQIRP system is found to go through a
backward bifurcation, which is a novel perspective for Coronavirus
infection transmission. The infection-free equilibrium and endemic
equilibrium are shown to be asymptotically stable globally using the
Lyapunov function hypothesis and the invariance principle of Lasalle.
A SQIRP system with backward bifurcation is explored using stochastic
analysis. The ecological stochasticity in the appearance of white
noise best describes the system’s value. To verify the results, more
numerical simulations are run.
to the modeling of interacting species in which prey has nonlinear repro-
duction, which is in competition with predator. The mathematical model's
stochastic stability is investigated. The method of designing appropriate
Lyapunov functions is used to identify permanence conditions among the
parameters of the model and conditions for the structure to no longer be
extinct. The system's two-dimensional di usive stability is regarded and
studied. The system experiences the process of saddle-node bifurcation
by varying the death rate of predator parameter. Further e ects of pa-
rameters that undergo inherent oscillations are numerically investigated,
revealing that as the intensity of predation parameter b is increased, the
device encounters non-periodic and damped oscillations.
proposed model in view of stability of the system with appropriate chosen attributes. Our findings are more focused on nanoparticle-induced aquatic ecosystem which may stabilize or destabilize the system, resulting in sensitive analysis through various parametric values. Furthermore, the depletion of nanoparticles from the aquatic system plays an important role for the steady coexistence of the host and commensal organisms, as contact rates between nanoparticles and hosts increase. Finally, the analytical results are verified and exposed through computer simulations which are quite interesting.
basic reproduction numbers. Hopf bifurcation is detected in the system, and a time delay is inserted in the transmission terms to represent the virus's incubation period. The spread of the novel COVID-19 strain to
humans is influenced by environmental conditions such as mugginess, precipitation, and temperature. To explore the impact of environmental oscillations on the coronavirus, we employ white noise perturbations in
the system. Finally, we examine the mathematical reenactments using MATLAB.
steadiness are indomitable. Finally, an ideal collecting strategy is conversed by applying Pontryagin’s maximal principle. It also addresses the steadiness of framework through mathematical reproduction utilizing MATLAB.
1993, followed by that in 1997; whereas it was a minimum in the year 1980, with an extension in its frequency in the subsequent years 1981 and 1982. The coefficient of variation of both annual and seasonal thunderstorm days is minimum over the areas of maximum frequency of mean thunderstorm days and vice-versa. The time-domain analysis confirms that the occurrence happened to be maximum in the year 1991, although each and every state did not witness thunderstorms every year. Also some other time-domain models like autocorrelation and seasonal integrated moving average provide adequate evidence for exploring the number of thunderstorms which happen to confirm the trend of
occurrence of thunderstorm over the years.
equations involving volatile compounds and microbial populations separately. TVB-N and TVC of stored rohu fish was determined at an interval of 4 days for 24 days. The initial and final biomass of TVB-N was 4.57 (fresh sample), 19.88 (24 days at 5◦C), and 7.10 mg/100 g (24th day at 0◦C), respectively. The TVC values were found to be 2.29 (fresh
sample), 9.5 (24 days at 5◦C) and 8.1 log (cfu/g) (24 days at 0◦C). Exponential, modified exponential, Howgate, and adapted Howgate models were considered for modeling the TVB-N formation, whereas logistic, modified logistic, Gompertz, and modified Gompertz
model were taken forward for modeling the microbial biomass developed in stored rohu fish. The exponential model found be the best fit model fit model for TVB-N prediction in rohu fish stored at 0 and 5◦C as it showed the highest R2 (0.9796, 0.9887) the lowest chi square
2 (0.2782, 0.3976), RMSE (0.52741, 0.6306) AIC (−7.3122, −4.8106), AICc (−0.5122, 1.9894) and BIC (−7.4204, −4.9188), respectively. The Gompertz model was found to be the best fit model for microbial biomass prediction in rohu fish stored at 5◦C (R2 = 0.9947, chi square
2 = 0.0537, AIC = −18.379, AICc = −6.3792 and BIC = −18.542), in
contrast, both of the logistic and modified logistic models were the best suited at 0◦C storage condition (R2 = 0.9919, chi square = 0.0823).