scholarly journals Qualitative analysis of a mathematical model about population of green turtles on the Galapagos island

BIOMATH ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 2107293
Author(s):  
Candy Herrera ◽  
Cosme Ramon Duque ◽  
Hugo Leiva
Keyword(s):  
Qualitative Analysis ◽  
Developmental Process ◽  
Sea Turtles ◽  
Continuous Model ◽  
Sea Turtle ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Sex Development ◽  
Turtle Population ◽  
Necessary And Sufficient

According to the IUCN, most sea turtles fall into one of the endangered categories. Since, sea turtles, like many other reptiles, present an unusual developmental process, marked by the determination of the sex of the offspring by environmental factors, more specifically by temperature. In the temperature sex determination (TSD) system the temperature of an embryo's environment during incubation period will dictate the embryo's sex development. This developmental process, together with the complex mating and nesting behavior and the vulnerability of sea turtles to threats of a natural or anthropogenic nature, naturally lead to the study of the population dynamics of the species.? For this reason, in this paper, we have developed a continuous model given by a system of three ordinary differential equations to study the dynamics of the green sea turtle population long-term, focusing the mathematical simulations on the data obtained for the nesting species of Galapagos Islands. Through the qualitative analysis of the model, the following is demonstrated: 1) The flow induced by the system is positively invariant on the region of biological interest and 2). The given condition on is necessary and sufficient for the unique nontrivial equilibrium point to be globally asymptotically stable in that region. When implementing the estimated values for our parameters in the numerical simulations, it was observed that indeed the population of Galapagos green sea turtles complies with the condition for which the nontrivial critical point is globally asymptotically stable.

scholarly journals The Impact of Temperature-Dependent Sex Determination on the Population Dynamics of Green Sea Turtles (Chelonia mydas)

Bionatura ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 1029-1038
Author(s):  
Candy Herrera ◽  
Evelyn Guerra ◽  
Andrea Rosas ◽  
Yingying Wei ◽  
Jack Pringle ◽  
...  
Keyword(s):  
Incubation Temperature ◽  
Sea Turtles ◽  
Sex Ratios ◽  
Chelonia Mydas ◽  
Continuous Model ◽  
Sea Turtle ◽  
Green Sea Turtle ◽  
Green Sea Turtles ◽  
Turtle Population ◽  
The Impact

The sex of the turtles is determined by the incubation temperature of the eggs during the mid-trimester of development. In green sea turtles (Chelonia mydas), recent studies show that sex ratios are changing, producing a female-biased sex ratio within the population. We developed a novel continuous model to analyze the dynamics of the green sea turtle population long-term. We determine the safe operating space for the proportion of eggs that become male at which the population of green sea turtle can exist without going to extinction. When the proportion of male eggs leaves this range the overall turtles’ population collapses. Additionally, we examined how temperature changes affect the sex ratios of the green sea turtle population.

scholarly journals Mathematical Modelling and Analysis of Corruption of Morals amongst Adolescents with Control Measures in Kenya

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Nathan Oigo Mokaya ◽  
Haileyesus Tessema Alemmeh ◽  
Cyrus Gitonga Ngari ◽  
Grace Gakii Muthuri
Keyword(s):  
Integrated Control ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Control Measures ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Appropriate ◽  
Manifold Theory ◽  
Necessary And Sufficient ◽  
Well Posed

In the present paper, we formulate a new mathematical model for the dynamics of moral corruption with comprehensive age-appropriate sexual information and provision of guidance and counselling. The population is subdivided into three (3) different compartments according to their level of information on sexual matters. The model is proved to be both epidemiologically and mathematically well posed. The existence of unique morally corrupt-free and endemic equilibrium points is investigated. The basic reproduction number with respect to morally corrupt-free equilibrium is obtained using next generation matrix approach to monitor the dynamics of corrupt morals and ascertain its level in order to suggest effective intervention strategies to control this problem. The local as well as global asymptotic stability of these equilibrium points is studied. The analysis reveals a globally asymptotically stable morally corrupt-free equilibrium whenever ℛ 0 ≤ 1 and a globally asymptotically stable endemic equilibrium if otherwise. Further analysis, using center manifold theory, shows that the model exhibits forward bifurcation insinuating that the classical epidemiological requirement of ℛ 0 ≤ 1 is necessary and sufficient for elimination of moral corruption. A brief discussion on the graphical results using the available numerical procedures is shown. From numerical simulations, it was ascertain that integrated control strategy is the best approach to fight against moral corruption transmission. Lastly, some key parameters that show significance in the moral corruption elimination from the society are also exploited.

scholarly journals Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Zhaofeng An ◽  
Suxia Zhang ◽  
Jinhu Xu
Keyword(s):  
Public Health ◽  
Health Education ◽  
Differential Equations ◽  
Discrete Model ◽  
Public Health Education ◽  
Continuous Model ◽  
Basic Reproductive Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nsfd Scheme

In this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the continuous equations. Threshold dynamics of the continuous model are performed by constructing Lyapunov functions. The analysis of a discrete model indicates that the alcohol-free equilibrium is globally asymptotically stable if the basic reproductive number R0<1, and conversely, the alcohol-present equilibrium is globally asymptotically stable if R0>1, revealing the consistency and efficiency of the discrete model to preserve the dynamical properties of the corresponding continuous model. In addition, stability preserving and the impact of the parameters related with public health education are conducted by numerical simulations.

scholarly journals Managing fisheries in a world with more sea turtles

2020 ◽  
Vol 287 (1930) ◽  
pp. 20200220
Author(s):  
Nathan F. Putman ◽  
Jesse Hawkins ◽  
Benny J. Gallaway
Keyword(s):  
Stock Assessment ◽  
Sea Turtles ◽  
Sea Turtle ◽  
Fishing Effort ◽  
Eastern United States ◽  
Green Turtles ◽  
Management Actions ◽  
Nesting Sites ◽  
Near Shore ◽  
Turtle Population

For decades, fisheries have been managed to limit the accidental capture of vulnerable species and many of these populations are now rebounding. While encouraging from a conservation perspective, as populations of protected species increase so will bycatch, triggering management actions that limit fishing. Here, we show that despite extensive regulations to limit sea turtle bycatch in a coastal gillnet fishery on the eastern United States, the catch per trip of Kemp's ridley has increased by more than 300% and green turtles by more than 650% (2001–2016). These bycatch rates closely track regional indices of turtle abundance, which are a function of increased reproductive output at distant nesting sites and the oceanic dispersal of juveniles to near shore habitats. The regulations imposed to help protect turtles have decreased fishing effort and harvest by more than 50%. Given uncertainty in the population status of sea turtles, however, simply removing protections is unwarranted. Stock-assessment models for sea turtles must be developed to determine what level of mortality can be sustained while balancing continued turtle population growth and fishing opportunity. Implementation of management targets should involve federal and state managers partnering with specific fisheries to develop bycatch reduction plans that are proportional to their impact on turtles.

Sedimentological characteristics of key sea turtle rookeries: potential implications under projected climate change

2010 ◽  
Vol 61 (4) ◽  
pp. 464 ◽  
Author(s):  
M. M. P. B. Fuentes ◽  
J. L. Dawson ◽  
S. G. Smithers ◽  
M. Hamann ◽  
C. J. Limpus
Keyword(s):  
Climate Change ◽  
Sea Turtles ◽  
Sea Turtle ◽  
Ecological Impacts ◽  
Coarse Grained ◽  
Sediment Characteristics ◽  
Emergence Success ◽  
Ecological Implications ◽  
Turtle Population ◽  
Reef Islands

Sea turtles rely on reef islands for key parts of their reproductive cycle and require specific sediment characteristics to incubate their eggs and dig their nests. However, little is known about the sedimentological characteristics of sea turtle rookeries, how these sediment characteristics affect the vulnerability of rookeries to climate change, and the ecological implications of different sediment or altered sediment characteristics to sea turtles. Therefore, we described the sediment and identified the reef-building organisms of the seven most important rookeries used by the northern Great Barrier Reef (nGBR) green turtle population. We then reviewed the literature on the vulnerability of each identified reef-building organism to climate change and how various sediment characteristics ecologically affect sea turtles. Sediments from the studied rookeries are predominantly composed of well-sorted medium-grained to coarse-grained sands and are either dominated by Foraminifera, molluscs or both. Dissimilarities in the contemporary sedimentology of the rookeries suggest that each may respond differently to projected climate change. Potential ecological impacts from climate change include: (1) changes in nesting and hatchling emergence success and (2) reduction of optimal nesting habitat. Each of these factors will decrease the annual reproductive output of sea turtles and thus have significant conservation ramifications.

scholarly journals Population dynamic between vulnerable coastal jaguars (Panthera onca) and endangered green sea turtles (Chelonia mydas) in Tortuguero National Park, Costa Rica.

2018 ◽  
Author(s):  
Stephanie Butera ◽  
Jaime Restrepo
Keyword(s):  
National Park ◽  
Sea Turtles ◽  
Chelonia Mydas ◽  
Sea Turtle ◽  
Predator Prey ◽  
Green Sea Turtles ◽  
Turtle Population ◽  
Nest Depredation ◽  
The Impact ◽  
Nest Predators

New-born sea turtles face a number of predators between the time the mothers lay eggs on the beach to when the hatchlings grow into larger juveniles. Nest depredation impacts reproductive success of nesting sea turtles, reducing the number of new turtles that make it to the sea. On Tortuguero beach nest predators include; dogs, coati, and raccoons. Nest depredation within Tortuguero National Park (TNP) has decreased dramatically since 1979. This decrease in nest depredation is linked to the increased jaguar population within TNP as the aforementioned species are considered the jaguars natural prey. Although jaguars prey on nesting turtles, they also control the populations of nest predators. Even more, jaguars have been demonstrated to change their behaviour to suit their preference in prey species therefore the nest predator distribution in TNP was examined to investigate whether changes in jaguar prey preference had an effect. Nest predation and the number of adult turtles lost to jaguar depredation were examined to determine the significance of the threat jaguars pose to the sea turtle population. This study investigates the predator prey relationship between jaguars, nest predators, and nesting female sea turtles; aiming to assessing the impact that jaguars have on the turtle's population.

scholarly journals Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model

2021 ◽  
Author(s):  
Manh Tuan Hoang
Keyword(s):  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Discrete Model ◽  
Reproduction Number ◽  
Continuous Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nsfd Scheme ◽  
The Basic Reproduction Number

The aim of this work is to study qualitative dynamical properties of a generalized hepatitis B epidemic model and its dynamically consistent discrete model. Positivity, boundedness, the basic reproduction number and asymptotic stability properties of the model are analyzed rigorously. By the Lyapunov stability theory and the Poincare-Bendixson theorem in combination with the Bendixson-Dulac criterion, we show that a disease-free equilibrium point is globally asymptotically stable if the basic reproduction number $\mathcal{R}_0 \leq 1$ and a disease-endemic equilibrium point is globally asymptotically stable whenever $\mathcal{R}_0 > 1$. Next, we apply the Mickens’ methodology to propose a dynamically consistent nonstandard finite difference (NSFD) scheme for the continuous model. By rigorously mathematical analyses, it is proved that the constructed NSFD scheme preserves essential mathematical features of the continuous model for all finite step sizes. Finally, numerical experiments are conducted to illustrate the theoretical findings and to demonstrate advantages of the NSFD scheme over standard ones. The obtained results in this work not only improve but also generalize some existing recognized works.

scholarly journals Effectiveness of Sea Turtle Conservation Management at the Turtle Conservation and Education Center of Serangan, Denpasar Bali

2021 ◽  
Vol 10 (1) ◽  
pp. 18
Author(s):  
Taurus Zeno Adi Eti Harnino ◽  
I Nyoman Yoga Parawangsa ◽  
Luthfiana Aprilianita Sari ◽  
Sulastri Arsad
Keyword(s):  
Sea Turtles ◽  
Marine Ecosystem ◽  
Sea Turtle ◽  
Sand Temperature ◽  
Observation Methods ◽  
Turtle Conservation ◽  
Sea Turtle Conservation ◽  
Nest Depth ◽  
Turtle Population ◽  
The Government

Turtles are one of the reptile animals that can migrate long distances along the Indian Ocean, Pacific Ocean and Southeast Asia. The purpose of turtle migration is to mate, find spawning locations and to find food. Sea turtles have an important role in maintaining the balance of the marine ecosystem. However, the high utilization of sea turtles by humans causes the turtle population to decline. One of the conservation sites that help the government program is in Serangan, Denpasar Bali, namely the TCEC (Turtle Conservation and Education Center), where there are several types of turtles such as the lekang turtle, hawksbill and green turtle. Data collection techniques in this study used observation methods including beach monitoring, relocation of turtle eggs to semi-natural hatchery hatching, hatchling and turtle nesting as well as measurement of turtle length and width carapase curve (CCL/CCW), sand temperature, nest depth, nest diameter, nest distance and nest calculation of the number of eggs to see the success of hatching. The results are turtle conservation activities, ranging from turtle maintenance, hatching of turtle eggs, relocation of eggs, and maintenance of hatchlings to release turtles. The effectiveness given by TCEC to manage and preserve the existence of sea turtles in Indonesia, especially in the Bali region is to provide awareness to the community by not consuming eggs and turtle meat.

Smaller longer, larger shorter: energy budget calculations explain intrapopulation variation in remigration intervals for loggerhead sea turtles (Caretta caretta)

2008 ◽  
Vol 86 (7) ◽  
pp. 595-600 ◽  
Author(s):  
Hideo Hatase ◽  
Katsumi Tsukamoto
Keyword(s):  
Feeding Habits ◽  
Sea Turtles ◽  
Caretta Caretta ◽  
Sea Turtle ◽  
Energy Budgets ◽  
Loggerhead Sea Turtles ◽  
Intrapopulation Variation ◽  
Turtle Population ◽  
The Difference ◽  
And Migration

Adult female loggerhead sea turtles ( Caretta caretta (L., 1758)) show a size-related behavioural and trophic dichotomy within several populations: oceanic planktivory by small females and neritic benthivory by large females. Within a Japanese population, smaller females have longer remigration intervals (the intervals between successive nesting years) than larger females. We hypothesized that this is attributed to the size-related foraging dichotomy, and calculated energy budgets and food requirements for the small and large females. Total reproductive energy costs for the small and large females were 1003 and 434 MJ, equivalent to 4043 kg of planktonic items and 275 kg of benthic items, respectively. The minimum durations necessary for accumulating the total reproductive energy for the small and large females were 430 and 26 days, equivalent to remigration intervals of 2 years and 1 year taking into account the nesting and migration durations and seasonal reproduction. Therefore, it was theoretically demonstrated that the intrapopulation variation in remigration intervals for Japanese loggerheads could be caused by the difference in their feeding habits, implying that remigration dynamics in a sea turtle population that shows a foraging dichotomy is regulated by feeding conditions not in a single habitat but in multiple habitats.

scholarly journals JUMLAH TEMPAT PENELURAN PENYU HIJAU (Chelonia mydas) BERDASARKAN VEGETASI PANTAI DI TAMAN WISATA ALAM (TWA) TANJUNG BELIMBING KECAMATAN PALOH KABUPATEN SAMBAS

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Wawan Kurniawan ◽  
Erianto Erianto ◽  
Iswan Dewantara
Keyword(s):  
Sea Turtles ◽  
Chelonia Mydas ◽  
Sea Turtle ◽  
Coastal Vegetation ◽  
Survey Method ◽  
Green Sea Turtle ◽  
Nature Tourism ◽  
Green Sea Turtles ◽  
Nesting Sites ◽  
Turtle Population

The decline in the population of green sea turtles (Chelonia mydas) occurs continuously due to the destruction of the nesting beach habitat, therefore efforts are needed to increase the green sea turtle population by rearranging nesting sites. One thing that is considered important from the green sea turtle nesting habitat is the coastal vegetation. This research was conducted in Tanjung Belimbing Nature Tourism Park, Sambas Regency, West Kalimantan Province. This study aims to obtain information on vegetation conditions that are preferred by green sea turtles to lay eggs through the number of nesting sites approach. The method used is a survey method. Data collection was carried out by direct observation in the field. In this study, 12 nesting sites were found spread over four observation sites, with the highest number of nesting site found at observation location 1 as many as 8 nesting sites. At observation location 1, besides cemara laut (Casuarina equisetifolia) and pandan laut (Pandanus tectorius) also found waru (Hibiscus tiliaceus) and api-api (Avicennia sp) as well as shrub plants such as kamboja laut (Scaevola taccada), serunai laut (Melanthera biflora) ) and herbal plants such as tapak kuda (Ipomoea pes-caprae), alaban tanah (Vitex rotundifolia), rumput tembaga (Ischaemum muticum), bayam berduri (Amaranthus sp) and bakung laut (Crynum asiaticum L).Keywords: Nesting Sites, Vegetation, Green sea turtle, Tanjung Belimbing Nature Tourism Park

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