Forecasting of Indian tourism industry using modeling approach.

Currently, India has become one of the largest economies of the world in which tourism and hospitality have significantly contributed; however, the growth rate of tourism industry has been greatly affected during the COVID-19 pandemic. In this study, we have used the modeling approach to analyze and understand the growth pattern of Indian tourism industry. To achieve this, we consider the data of international tourist arrivals before and after the lockdown. The Dickey-Fuller test, AIC and BIC methods are used to obtain the best fitted model and further, the accuracy of obtained model is also analyzed. Data and forecasting indicate that the weather and public holidays significantly affect the tourism industry.

Modeling the impact of hospital beds and vaccination on the dynamics of an infectious disease.

The unprecedented scale and rapidity of dissemination of re-emerging and emerging infectious diseases impose new challenges for regulators and health authorities. To curb the dispersal of such diseases, proper management of healthcare facilities and vaccines are core drivers. In the present work, we assess the unified impact of healthcare facilities and vaccination on the control of an infectious disease by formulating a mathematical model. To formulate the model for any region, we consider four classes of human population; namely, susceptible, infected, hospitalized, and vaccinated. It is assumed that the increment in number of beds in hospitals is continuously made in proportion to the number of infected individuals. To ensure the occurrence of transcritical, saddle-node and Hopf bifurcations, the conditions are derived. The normal form is obtained to show the existence of Bogdanov-Takens bifurcation. To validate the analytically obtained results, we have conducted some numerical simulations. These results will be useful to public health authorities for planning appropriate health care resources and vaccination programs to diminish prevalence of infectious diseases.

Modeling the role of renewable energy to mitigate the atmospheric level of carbon dioxide along with sustainable development.

In the past few decades, the use of fossil fuels has increased dramatically due to industrialization in developing nations. The elevation of carbon dioxide (CO2) has become a serious concern for the entire world. Therefore, most countries want to reduce the use of fossil fuels by transitioning to renewable energy sources. In this research work, we formulate a nonlinear mathematical model to study the interplay between atmospheric CO2, human population, and energy production through traditional energy sources (coal, oil, and gas) and renewable energy sources (solar, wind, and hydro). For the model formulation, we consider that the atmospheric level of CO2 increases due to human activities and energy production through traditional energy sources. Additionally, we consider that the dependency of the human population shifts from traditional to renewable sources of energy as the atmospheric level of CO2 increases. Through the model analysis, we have obtained a condition that implies a change in the equilibrium level of CO2 by increasing the deployment rate of renewable energy sources. This condition demonstrates that the atmospheric level of CO2 can be reversed from its current level through sufficient deployment of renewable energy sources. Moreover, for a certain critical value of the growth rate parameter of renewable energy, three interior equilibria may exist. This situation indicates the presence of hysteresis, which implies that the system may undergo discontinuous jumps between different stable steady states. Furthermore, we discuss an optimal control problem to minimize atmospheric CO2, simultaneously minimizing the cost of the considered strategy.

Allocation of hospital beds on the emergence of new infectious disease: A mathematical model.

This paper is concerned to a mathematical model for the management of hospital beds when a new infection emerges in the population with the existing infections. The study of this joint dynamics presents formidable mathematical challenges due to a limited number of hospital beds. We have derived the invasion reproduction number, which investigates the potential of a newly emerged infectious disease to persist when some infectious diseases are already invaded the host population. We have shown that the proposed system exhibits transcritical, saddle-node, Hopf, and Bogdanov-Takens bifurcations under certain conditions. We have also shown that the total number of infected individuals may increase if the fraction of the total number of hospital beds is not properly allotted to the existing and a newly emerged infectious disease. The analytically obtained results are verified with the help of numerical simulations.

Modeling the impact of precautionary measures and sanitation practices broadcasted through media on the dynamics of bacterial diseases.

The media has a significant contribution in spreading awareness by broadcasting various programs about prevalent diseases in the society along with the role of providing information, feeding news and educating a large mass. In this paper, the effect of media programs promoting precautionary measures and sanitation practices to control the bacterial infection in the community is modeled and analyzed considering the number of media programs as a dynamical variable. In the modeling phenomena, human population is partitioned into three classes; susceptible, infected and recovered. The disease is supposed to spread by direct contact of susceptible with infected individuals and indirectly by the ingestion of bacteria present in the environment. The growth in the media programs is considered proportional to the size of infected population and the impact of these programs on the indirect disease transmission rate and bacteria shedding rate by infected individuals is also considered. The feasibility of equilibria and their stability conditions are obtained. Model analysis reveals that broadcasting media programs and increasing its effectiveness shrink the size of infected class and control the spread of disease to a large extent.

Potential use of Tinospora cordifolia as a herbal supplement in dairy animals: a review.

Supplementation is an integral part of modern dairy-feeding practices which mainly emphasise on higher production. Different supplements have been utilized by the farmers according to the need and action of supplements. Tinospora cordifolia (TC) is one such herbal supplement which can be utilized to feed dairy animals either alone or in combination with other supplements. TC is a herb found in tropical countries and having number of medicinal properties. Beneficial health effects of TC include immunostimulation, protection against inflammation and bacterial action, hepatoprotection, antioxidant and antineoplastic effects. Available studies on TC supplementation in dairy animals have shown a positive effect on health, body parameters and production performance. Supplementing TC is economically feasible, and it can be adopted by farmers as it helps in improving their net income. However, more research is needed in the field of dairy animals to explore the full potential of this herb. This review is written with the objective of highlighting the possibilities of using TC in dairy animal rations and promoting research in the concerned field to fill the gaps in knowledge. Thorough knowledge about TC and its effect in dairy animals can add a new concept to the supplementation process and developments of dairy rations.

Modeling the impact of social media on the adoption of a new product by customers.

Marketers and entrepreneurs need to keep up with the fast-paced changes that are happening in the business environment, or they might face the risk of becoming obsolete in the rapidly changing business environment. It is long gone the days when a conventional business model used to help grow fast and get success. With the emergence of social media, the role of consumer-to-consumer communication about the new products and the firms that produce them has been highly magnified in the marketplace. Social media advertisements are promising tools that affect the adoption of a new product. In this paper, a non-linear mathematical model is introduced for this study. To perceive the impact of social media advertisements on the adoption of a new product, we have considered three dynamic variables; namely, (i) non-adopting population, (ii) adopting population, and (iii) social media advertisements. The stability theory of differential equations has been used to study the model analytically. The computer generated figures are drawn in support of derived analytical results for a particular set of parameter values.•We have proposed and analyzed an nonlinear mathematical model to study the impact of social media advertisements on adoption of new product.•We have considered three dynamical variables; namely, non-adopting population, adopting population, and social media advertisements.•The stability theory of differential equations has been used to study the model analytically.

Modeling the effect of time delay in the increment of number of hospital beds to control an infectious disease.

One of the key factors to control the spread of any infectious disease is the health care facilities, especially the number of hospital beds. To assess the impact of number of hospital beds and control of an emerged infectious disease, we have formulated a mathematical model by considering population (susceptible, infected, hospitalized) and newly created hospital beds as dynamic variables. In formulating the model, we have assumed that the number of hospital beds increases proportionally to the number of infected individuals. It is shown that on a slight change in parameter values, the model enters to different kinds of bifurcations, e.g., saddle-node, transcritical (backward and forward), and Hopf bifurcation. Also, the explicit conditions for these bifurcations are obtained. We have also shown the occurrence of Bogdanov-Takens (BT) bifurcation using the Normal form. To set up a new hospital bed takes time, and so we have also analyzed our proposed model by incorporating time delay in the increment of newly created hospital beds. It is observed that the incorporation of time delay destabilizes the system, and multiple stability switches arise through Hopf-bifurcation. To validate the results of the analytical analysis, we have carried out some numerical simulations.

Modeling the importance of temporary hospital beds on the dynamics of emerged infectious disease.

To explore the impact of available and temporarily arranged hospital beds on the prevention and control of an infectious disease, an epidemic model is proposed and investigated. The stability analysis of the associated equilibria is carried out, and a threshold quantity basic reproduction number ( R0) that governs the disease dynamics is derived and observed whether it depends both on available and temporarily arranged hospital beds. We have used the center manifold theory to derive the normal form and have shown that the proposed model undergoes different types of bifurcations including transcritical (backward and forward), Bogdanov-Takens, and Hopf-bifurcation. Bautin bifurcation is obtained at which the first Lyapunov coefficient vanishes. We have taken advantage of Sotomayor's theorem to establish the saddle-node bifurcation. Numerical simulations are performed to support the theoretical findings.

Effect of bypass fatty acid and Tinospora cordifolia supplementation on production performance and milk fatty acid profiling in Murrah buffaloes (Bubalus bubalis).

Buffaloes contribute about 49% of total milk production and are considered as major milk-producing animals in India. During the early stage of lactation, mostly high producing animals suffer from negative energy balance (NEB) due to imbalance between the needs and availability of energy, and this NEB has a negative impact on production and health of buffaloes. Taking this into consideration, a study was conducted at National Dairy Research Institute, Karnal on 20 freshly calved healthy Murrah buffaloes (Bubalus bubalis). Buffaloes were grouped depending on their previous milk yield, body weight, and parity as T0 (control), T1 (fatty acids), T2 (Tinospora), and T3 (mix) groups having five animals each. Supplementation of 150 g of bypass fatty acids in T1 group, 150 g of Tinospora powder in T2 group, and combination of 150 of bypass fatty acid and 150 g of Tinospora powder in T3 group over and above the standard feeding schedule was done for a duration of 90 days whereas standard feeding schedule was followed in T0 group. A significant (P < 0.05) increase in average daily milk yield was observed in T1 (10.06 ± 0.56 kg/d/h), T2 (10.30 ± 0.53 kg/d/h), and T3 (10.11 ± 0.48 kg/d/h) in comparison to control group (8.05 ± 0.38 kg/d/h). Significantly (P < 0.05) higher milk fat percent and total solids were also recorded in treatment groups over the control group. Other milk constituents (SNF, protein, lactose, ash) and milk properties (pH, conductivity, freezing point, density) remained unaffected by the supplementations. The somatic cell count values were significantly (P < 0.05) decreased in T2 and T3 with the advancement in the lactation in comparison to T0 and T1. Supplementation also leads to significantly (P < 0.05) higher MUFA and PUFA contents in milk of treatment group buffaloes in comparison to control group. The study outcomes state that combination of bypass fatty acids and Tinospora cordifolia supplementation improves milk production and its composition in lactating Murrah buffaloes.

An optimal control problem for carrier dependent diseases.

In developing countries, several diseases spread in human population due to the abundance of houseflies (a kind of carrier). The main reason behind the spread of these diseases is the lack of awareness among peoples regarding the sanitation practices and economic constraints. To understand the dynamics of the spread and control of these diseases, in this paper, we propose a mathematical model by considering logistic growth of houseflies. In the model formulation, it is assumed that houseflies transport the bacteria responsible for the disease transmission from the environment to the edibles of human population. To reduce the density of houseflies and number of infected individuals, an optimization problem is also formulated and analyzed. Numerical simulations are performed to support analytically obtained results.

Modeling the Effect of Prey Refuge on a Ratio-Dependent Predator-Prey System with the Allee Effect.

The extinction of species is a major threat to the biodiversity. The species exhibiting a strong Allee effect are vulnerable to extinction due to predation. The refuge used by species having a strong Allee effect may affect their predation and hence extinction risk. A mathematical study of such behavioral phenomenon may aid in management of many endangered species. However, a little attention has been paid in this direction. In this paper, we have studied the impact of a constant prey refuge on the dynamics of a ratio-dependent predator-prey system with strong Allee effect in prey growth. The stability analysis of the model has been carried out, and a comprehensive bifurcation analysis is presented. It is found that if prey refuge is less than the Allee threshold, the incorporation of prey refuge increases the threshold values of the predation rate and conversion efficiency at which unconditional extinction occurs. Moreover, if the prey refuge is greater than the Allee threshold, situation of unconditional extinction may not occur. It is found that at a critical value of prey refuge, which is greater than the Allee threshold but less than the carrying capacity of prey population, system undergoes cusp bifurcation and the rich spectrum of dynamics exhibited by the system disappears if the prey refuge is increased further.

The role of algae in agriculture: a mathematical study.

Synthetic fertilizers and livestock manure are nowadays widely used in agriculture to improve crop yield but nitrogen and phosphorous runoff resulting from their use compromises water quality and contributes to eutrophication phenomena in waterbeds within the countryside and ultimately in the ocean. Alternatively, algae could play an important role in agriculture where they can be used as biofertilizers and soil stabilizers. To examine the possible reuse of the detritus generated by dead algae as fertilizer for crops, we develop three mathematical models building upon each other. A system is proposed in which algae recover waste nutrients (nitrogen and phosphorus) for reuse in agricultural production. The results of our study show that in so doing, the crop yield may be increased and simultaneously the density of algae in the lake may be reduced. This could be a way to mitigate and possibly solve the environmental and economic issues nowadays facing agriculture.

Genetic diversity and structure in hill rice (Oryza sativa L.) landraces from the North-Eastern Himalayas of India.

BACKGROUND: Hill rices (Oryza sativa L.) are direct seeded rices grown on hill slopes of different gradients. These landraces have evolved under rainfed and harsh environmental conditions and may possess genes governing adaptation traits such as tolerance to cold and moisture stress. In this study, 64 hill rice landraces were collected from the state of Arunachal Pradesh of North-Eastern region of India, and assessed by agro-morphological variability and microsatellite markers polymorphism. Our aim was to use phenotypic and genetic diversity data to understand the basis of farmers' classification of hill rice landraces into two groups: umte and tening. Another goal was to understand the genetic differentiation of hill rices into Indica or japonica subspecies. RESULTS: According to farmers' classification, hill rices were categorized into two groups: umte (large-grained, late maturing) and tening (small-grained, early maturing). We did not find significant difference in days to 50 % flowering between the groups. Principal component analysis revealed that two groups can be distinguished on the basis of kernel length-to-width ration (KLW), kernel length (KL), grain length (GrL), grain length-to-width ration (GrLW) and plant height (Ht). Stepwise canonical discriminant analysis identified KL and Ht as the main discriminatory characters between the cultivar groups. Genetic diversity analysis with 35 SSR markers revealed considerable genetic diversity in the hill rice germplasm (gene diversity: 0.66; polymorphism information content: 0.62). Pair-wise allelic difference between umte and tening groups was not statistically significant. The model-based population structure analysis showed that the hill rices were clustered into two broad groups corresponding to Indica and Japonica. The geographic distribution and cultivars grouping of hill rices were not congruent in genetic clusters. Both distance- and model-based approaches indicated that the hill rices were predominantly japonica or admixture among the groups within the subspecies. These findings were further supported by combined analysis hill rices with 150 reference rice accessions representing major genetic groups of rice. CONCLUSION: This study collected a valuable set of hill rice germplasm for rice breeding and for evolutionary studies. It also generated a new set of information on genetic and phenotypic diversity of hill rice landraces in North-Eastern region of India. The collected hill rices were mostly japonica or admixture among the subpopulations of Indica or Japonica. The findings are useful for utilization and conservation of hill rice germplasm.

Development of CAPS markers to identify Indian tea (Camellia sinensis) clones with high catechin content.

Tea leaves are rich in plant secondary phenolics, especially flavonoids. Catechins are considered to be the most valuable flavonoids, and the catechin content in tea is an important trait for determining its quality. We have developed cleaved amplified polymorphic sequence (CAPS)-based markers for evaluating total catechin content that target two important secondary metabolite pathway genes, PAL (phenylalanine ammonia-lyase) and CHS (chalcone synthase). Catechin content levels in the tea samples tested ranged from 9 to 33 mg/mg. The CAPS technique identified clones with the homozygous profile PRc1, which has relatively lower catechin content than clones with the heterozygous profile PRc2. A significant difference (t = 16.85) in the level of catechin content was also detected between heterozygotes and homozygotes in the tea seed stock TS379. We found a polynomial relationship between the marker developed for CHS2 and catechin content in these tea samples with R2 = 0.9788. Moreover, PAL has less of a relationship with catechin content. Therefore, we recommend tea clones with heterozygous CAPS profiles for the gene CHS2+RcaI for the further improvement in these clones.

Modeling the impact of awareness on the mitigation of algal bloom in a lake.

The proliferation of algal bloom in water bodies due to the enhanced concentration of nutrient inflow is becoming a global issue. A prime reason behind this aquatic catastrophe is agricultural runoff, which carries a large amount of nutrients that make the lakes more fertile and cause algal blooms. The only solution to this problem is curtailing the nutrient loading through agricultural runoff. This could be achieved by raising awareness among farmers to minimize the use of fertilizers in their farms. In view of this, in this paper, we propose a mathematical model to study the effect of awareness among the farmers of the mitigation of algal bloom in a lake. The growth rate of awareness among the farmers is assumed to be proportional to the density of algae in the lake. It is further assumed that the presence of awareness among the farmers reduces the inflow rate of nutrients through agricultural runoff and helps to remove the detritus by cleaning the bottom of the lake. The results evoke that raising awareness among farmers may be a plausible factor for the mitigation of algal bloom in the lake. Numerical simulations identify the most critical parameters that influence the blooms and provide indications to possibly mitigate it.

Stability analysis and optimal control of an epidemic model with awareness programs by media.

The impact of awareness campaigns and behavioral responses on epidemic outbreaks has been reported at times. However, to what extent does the provision of awareness and behavioral changes affect the epidemic trajectory is unknown, but important from the public health standpoint. To address this question, we formulate a mathematical model to study the effect of awareness campaigns by media on the outbreak of an epidemic. The awareness campaigns are treated as an intervention for the emergent disease. These awareness campaigns divide the whole populations into two subpopulation; aware and unaware, by inducing behavioral changes amongst them. The awareness campaigns are included explicitly as a separate dynamic variable in the modeling process. The model is analyzed qualitatively using stability theory of differential equations. We have also identified an optimal implementation rate of awareness campaigns so that disease can be controlled with minimal possible expenditure on awareness campaigns, using optimal control theory. The control setting is investigated analytically using optimal control theory, and the numerical solutions illustrating the optimal regimens under various assumptions are also shown.

Genetic Diversity and Population Structure in Aromatic and Quality Rice (Oryza sativa L.) Landraces from North-Eastern India.

The North-eastern (NE) India, comprising of Arunachal Pradesh, Assam, Manipur, Meghalaya, Mizoram, Nagaland, Sikkim and Tripura, possess diverse array of locally adapted non-Basmati aromatic germplasm. The germplasm collections from this region could serve as valuable resources in breeding for abiotic stress tolerance, grain yield and cooking/eating quality. To utilize such collections, however, breeders need information about the extent and distribution of genetic diversity present within collections. In this study, we report the result of population genetic analysis of 107 aromatic and quality rice accessions collected from different parts of NE India, as well as classified these accessions in the context of a set of structured global rice cultivars. A total of 322 alleles were amplified by 40 simple sequence repeat (SSR) markers with an average of 8.03 alleles per locus. Average gene diversity was 0.67. Population structure analysis revealed that NE Indian aromatic rice can be subdivided into three genetically distinct population clusters: P1, joha rice accessions from Assam, tai rices from Mizoram and those from Sikkim; P2, aromatic rice accessions from Nagaland; and P3, chakhao rice germplasm from Manipur [corrected]. Pair-wise FST between three groups varied from 0.223 (P1 vs P2) to 0.453 (P2 vs P3). With reference to the global classification of rice cultivars, two major groups (Indica and Japonica) were identified in NE Indian germplasm. The aromatic accessions from Assam, Manipur and Sikkim were assigned to the Indica group, while the accessions from Nagaland exhibited close association with Japonica. The tai accessions of Mizoram along with few chakhao accessions collected from the hill districts of Manipur were identified as admixed. The results highlight the importance of regional genetic studies for understanding diversification of aromatic rice in India. The data also suggest that there is scope for exploiting the genetic diversity of aromatic and quality rice germplasm of NE India for rice improvement.

Spatial dynamics of a nutrient-phytoplankton system with toxic effect on phytoplankton.

The production of toxins by some species of phytoplankton is known to have several economic, ecological, and human health impacts. However, the role of toxins on the spatial distribution of phytoplankton is not well understood. In the present study, the spatial dynamics of a nutrient-phytoplankton system with toxic effect on phytoplankton is investigated. We analyze the linear stability of the system and obtain the condition for Turing instability. In the presence of toxic effect, we find that the distribution of nutrient and phytoplankton becomes inhomogeneous in space and results in different patterns, like stripes, spots, and the mixture of them depending on the toxicity level. We also observe that the distribution of nutrient and phytoplankton shows spatiotemporal oscillation for certain toxicity level.