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In this paper, we explore the bifurcation, chaos, and local stability of a discrete Hepatitis C virus infection model. More precisely, we studied the local stability at fixed points of a discrete Hepatitis C virus model. We proved that at a partial infection fixed point, the discrete HCV model undergoes Neimark-Sacker bifurcation, but no other local bifurcation exists at this fixed point. Moreover, it was also proved that period-doubling bifurcation does not occur at liver-free, disease-free, and total infection fixed points. Furthermore, we also examined chaos control in the understudied discrete HCV model. Finally, obtained theoretical results were confirmed numerically.

Mathematical models play a crucial role in understanding the dynamics of epidemic diseases by providing insights into how they spread and be controlled. In biomathematics, mathematical modeling is a powerful tool for interpreting the experimental results of biological phenomena related to disease transmission, offering precise and quantitative insights into the processes involved. This paper focused on a discrete mathematical model of the Hepatitis C virus (HCV) to analyze its dynamical behavior. Initially, we examined the local dynamics at steady states, providing a foundation for understanding the system's stability under various conditions. We then conducted a detailed bifurcation analysis, revealing that the discrete HCV model undergoes a Neimark-Sacker bifurcation at the uninfected steady state. Notably, our analysis showed that no period-doubling or fold bifurcations occur at this state. Further investigation at the infected steady state demonstrated the presence of both period-doubling and Neimark-Sacker bifurcations, which are characterized using explicit criteria. By employing a feedback control strategy, we explored chaotic behavior within the HCV model, highlighting the complex dynamics that can arise under certain conditions. Numerical simulations were conducted to verify the theoretical results, illustrating the model's validity and applicability. From a biological perspective, the insights gained from this analysis enhance our understanding of HCV transmission dynamics and potential intervention strategies. The presence of Neimark-Sacker bifurcation at the uninfected steady state implies that small perturbations could lead to oscillatory behavior, which may correspond to fluctuations in the number of infections over time. This finding suggests that maintaining stability at this steady state is critical for preventing outbreaks. The period-doubling and Neimark-Sacker bifurcations at the infected steady state indicate the potential for more complex oscillatory patterns, which could represent persistent cycles of infection and remission in a population. Finally, exploration of chaotic dynamics through feedback control highlights the challenges in predicting disease spread and the need for careful management strategies to avoid chaotic outbreaks.

In this paper, we explore local dynamics at equilibrium points, the existence of bifurcation sets and codimension-one bifurcation analysis of a discrete prey–predator system with Holling type-II functional response. Further, OGY and Hybrid control strategies are utilized to control chaos in the under study discrete model due to the occurrence of Neimark–Sacker and flip bifurcations. Finally, numerical simulations are given to verify theoretical results.

In this paper, we have delved into the intricate dynamics of a discrete-time Hepatitis B virus (HBV) model, shedding light on its local dynamics, topological classifications at equilibrium states, and pivotal epidemiological parameters such as the basic reproduction number. Our analysis extended to exploring convergence rates, control strategies, and bifurcation phenomena crucial for understanding the behavior of the HBV system. Employing linear stability theory, we meticulously examined the local dynamics of the HBV model, discerning various equilibrium states and their topological classifications. Subsequently, we identified bifurcation sets at these equilibrium points, providing insights into the system's stability and potential transitions. Further, through the lens of bifurcation theory, we conducted a comprehensive bifurcation analysis, unraveling the intricate interplay of parameters that govern the HBV model's behavior. Our investigation extended beyond traditional stability analysis to explore chaos and convergence rates, enriching our understanding of the dynamics of the understudied HBV model. Finally, we validated our theoretical findings through numerical simulations, confirming the robustness and applicability of our analysis in real-world scenarios. By integrating biological and epidemiological insights into our mathematical framework, we offered a holistic understanding of the dynamics of HBV transmission dynamics, with implications for public health interventions and disease control strategies.

Abstract Spider silk exhibits an excellent combination of high strength and toughness, which originates from the hierarchical self-assembled structure of spidroin during fiber spinning. In this work, superfine nanofibrils are established in polyelectrolyte artificial spider silk by optimizing the flexibility of polymer chains, which exhibits combination of breaking strength and toughness ranging from 1.83 GPa and 238 MJ m−3 to 0.53 GPa and 700 MJ m−3, respectively. This is achieved by introducing ions to control the dissociation of polymer chains and evaporation-induced self-assembly under external stress. In addition, the artificial spider silk possesses thermally-driven supercontraction ability. This work provides inspiration for the design of high-performance fiber materials.

In this paper, we examined the codimension-two bifurcation analysis of a two-dimensional discrete epidemic model. More precisely, we examined the codimension-two bifurcation analysis at an endemic equilibrium state associated with $ 1:2 $, $ 1:3 $ and $ 1:4 $ strong resonances by bifurcation theory and series of affine transformations. Finally, theoretical results were carried out numerically.

Abstract Spider silk, possessing exceptional combination properties, is classified as a bio‐gel fiber. Thereby, it serves as a valuable origin of inspiration for the advancement of various artificial gel fiber materials with distinct functionalities. Gel fibers exhibit promising potential for utilization in diverse fields, including smart textiles, artificial muscle, tissue engineering, and strain sensing. However, there are still numerous challenges in improving the performance and functionalizing applications of spider silk‐inspired artificial gel fibers. Thus, to gain a penetrating insight into bioinspired artificial gel fibers, this review provided a comprehensive overview encompassing three key aspects: the fundamental design concepts and implementing strategies of gel fibers, the properties and strengthening strategies of gel fibers, and the functionalities and application prospects of gel fibers. In particular, multiple strengthening and toughening mechanisms were introduced at micro, nano, and molecular‐level structures of gel fibers. Additionally, the existing challenges of gel fibers are summarized. This review aims to offer significant guidance for the development and application of artificial gel fibers and inspire further research in the field of high‐performance gel fibers.

This study explores the Ivancevic Option Pricing Model, a nonlinear wave-based alternative to the Black-Scholes model, using adaptive nonlinear Schrödingerr equations to describe the option-pricing wave function influenced by stock price and time. Our focus is on a comprehensive analysis of this equation from multiple perspectives, including the study of soliton dynamics, chaotic patterns, wave structures, Poincaré maps, bifurcation diagrams, multistability, Lyapunov exponents, and an in-depth evaluation of the model's sensitivity. To begin, a wave transformation is applied to convert the partial differential equation into an ordinary differential equation, from which soliton solutions are derived using the [Formula: see text] method. We explore various forms of the option price function at different time points, including singular-kink, periodic, hyperbolic, trigonometric, exponential, and complex solutions. Furthermore, we simulate 3D surface plots and 2D graphs for the real, imaginary, and modulus components of some of the obtained solutions, assigning specific parameter values to enhance visualization. These graphical representations offer valuable insights into the dynamics and patterns of the solutions, providing a clearer understanding of the model's behavior and potential applications. Additionally, we analyze the system's dynamic behavior when a perturbing force is introduced, identifying chaotic patterns using the Lyapunov exponent, Sensitivity, multistability analysis, RK4 method, wave structures, bifurcation diagrams, and Poincaré maps.

We study the existence of fixed points, local stability analysis, bifurcation sets at fixed points, codimension-one and codimension-two bifurcation analysis, and chaos control in a predator-prey model with Holling types I and III functional responses. It is proven that the model has a trivial equilibrium point for all involved parameters but interior and semitrivial equilibrium solutions under certain model parameter conditions. Furthermore, local stability at trivial, semitrivial, and interior equilibria using the theory of linear stability is investigated. We have also explored the bifurcation sets for trivial, semitrivial, and interior equilibria and proved that flip bifurcation occurs at semitrivial equilibrium. Furthermore, it is also proven that Neimark–Sacker bifurcation as well as flip bifurcation occurs at an interior equilibrium solution, and in addition, at the same equilibrium solution, we also studied codimension-two 1:2 strong resonance bifurcation. Then, OGY and hybrid control strategies are employed to manage chaos in the model under study, which arises from Neimark–Sacker and flip bifurcations, respectively. We have also examined the preservation of the positive solution of the understudied model. Finally, numerical simulations are given to verify the theoretical results.

Background: Temporomandibular patients frequently feel discomfort in other areas as well. It is believed that temporomandibular dysfunction (TMD) is linked to whole body imbalance including lower cervical and upper thoracic spine. Objective: To determine the relationship between lower cervical and upper thoracic spine with TMJ disorders. Methodology: This study was conducted on bilateral temporomandibular disorder patients of Multan. It included both males and females of age group between 20 to 50 years. People with history of trauma and fracture of face, patients with any spine abnormality and systemic disease such as rheumatoid were excluded. Helkimo index, neck disability scale and Oswestry scale was used to assess TMJ, cervical spine and thoracic spine. Results: In the current study total of 82 participants participated with a mean age of 31.19. In this study, 31(37.8%) males and 51(62.2%) females participated for the study. Result showed that there are 32 (39%) with mild dysfunction, 28 (34.1%) with moderate dysfunction and 22 (26.8%) with severe dysfunction of TMJ. Neck disability scale results showed that around 21 (25.6%) had no disability, 25 (30.5%) had mild disability, 19 (23.2%) had moderate, 16 (19.5%) had severe and only 1 (1.2%) had total disability of neck and Oswestry disability index results showed that the 53 (64.6%) had mild thoracic spine disability, 16 (19.5%) had moderate thoracic spine disability and 13 (15.9%) had severe thoracic spine disability of thoracic spine. Association was found between TMJ dysfunctions with both cervical spine and thoracic spine (P

Background: Shoulder pain is the most common health related problem. Diabetic patients are also exposed and appeared to have prevalent shoulder pain due to diabetics and physical stress. Many other causes such as trauma, injury, bursitis, tendinitis is included. In this study, we analyzed the frequency of shoulder pain in diabetic patients. Objective: To find out the frequency of shoulder pain in type 2 diabetes mellitus patients in Multan. Methodology: It was a cross sectional study. Data was collected from different areas of Multan. The sample size was 120 patients which were selected through convenient sampling. Shoulder Pain and Disability Index (SPADI) was used to find out the frequency. Sample selection was computed through Cochran’s formula. The data was analyzed by SPSS 21.0 Version. Results: Total sample size was 120 out of which there were 52 participants who had shoulder pain and 68 participants did not report shoulder pain. 57% diabetics with shoulder pain who reported no difficulty during clothing. 32% reported that they had mild level of difficulty during clothing and 11% reported moderate level difficulty during clothing due to shoulder pain However, there were no one who reported severe level of difficulty during clothing due to shoulder pain. 31.67% participants who reported mild level of difficulty during reaching. 10% reported moderate level of difficulty and 2% reported severe level of difficulty during reaching activities whereas 57% reported having no difficulty in reaching. The mean of total SPADI score was 84.92. Conclusion: The study investigated shoulder pain in Type 2 diabetes patients, assessing external rotation and glycated HbA1c levels. It emphasizes the importance of addressing musculoskeletal issues in diabetes management and promoting better understanding and treatment of shoulder pain in these patients.

Abstract It is highly desirable to develop fiber materials with high strength and toughness while increasing fiber strength always results in a decrease in toughness. Spider silk is a natural fiber material with an excellent combination of high strength and toughness, which is produced from the spinning dope solution by gelation and drawing spinning process. This encourages people to prepare artificial fibers by mimicking the material, structure, and spinning of natural spider silk. In this review, we first summarized the preparation of artificial spider silk prepared via such a gelation process from different types of materials, including nonrecombinant proteins, recombinant proteins, polypeptides, synthetic polymers, and polymer nanocomposites. In addition, different spinning approaches for spinning artificial spider silk are also summarized. In the third section, some novel application scenarios of the artificial spider silk were summarized, such as artificial muscles, sensing, and smart fibers.

In this paper, we explore the existence of fixed points, local dynamical characteristics at fixed points, the existence of bifurcation sets at fixed points, and bifurcations of a three-species discrete prey-predator system with the scavenger. More specifically, it is proved that for all parameters, the discrete system has trivial and boundary fixed points; two more boundary fixed points, and an interior fixed point under a certain model's parametric restriction(s). Further, by the theory of linear stability, we examined local dynamics at fixed points. In order to understand the dynamics of the understudied system thoroughly, we studied the occurrence of certain bifurcations at fixed points by the bifurcation theory. Finally, theoretical results are numerically verified.

The boundedness character, persistent nature, and asymptotic conduct of non-negative outcomes of the system of three dimensional exponential form of difference equations were studied in this research: $ \begin{eqnarray*} x_{n+1} & = &ax_{n}+by_{n-1}e^{-x_{n}}, \\ \text{ }y_{n+1} & = &cy_{n}+dz_{n-1}e^{-y_{n}},\ \\ z_{n+1} & = &ez_{n}+fx_{n-1}e^{-z_{n}}, \end{eqnarray*} $ where $ a, \ b, \ c $, $ d, \ e $ and $ f $ are non-negative real values, and the initial values $ x_{-1}, \ x_{0}, \ y_{-1}, \ y_{0}, \ z_{-1}, \ z_{0} $ are non-negative real values.

We explore the local dynamical characteristics, chaos and bifurcations of a two-dimensional discrete laser model in $ \mathbb{R}_+^2 $. It is shown that for all $ a $, $ b $, $ c $ and $ p $, model has boundary fixed point $ P_{0y}(0, \frac{p}{c}) $, and the unique positive fixed point $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $ if $ p > \frac{b c}{a} $. Further, local dynamical characteristics with topological classifications for the fixed points $ P_{0y}(0, \frac{p}{c}) $ and $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $ have explored by stability theory. It is investigated that flip bifurcation exists for the boundary fixed point $ P_{0y}(0, \frac{p}{c}) $, and also there exists a flip bifurcation if parameters vary in a small neighborhood of the unique positive fixed point $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $. Moreover, it is also explored that for the fixed point $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $, laser model undergoes a Neimark-Sacker bifurcation, and in the meantime stable invariant curve appears. Numerical simulations are implemented to verify not only obtain results but also exhibit complex dynamics of period $ -2 $, $ -3 $, $ -4 $, $ -5 $, $ -8 $ and $ -9 $. Further, maximum lyapunov exponents along with fractal dimension are computed numerically to validate chaotic behavior of the laser model. Lastly, feedback control method is utilized to stabilize chaos exists in the model.

In this paper, we explore local dynamic characteristics, bifurcations and control in the discrete activator-inhibitor system. More specifically, it is proved that discrete-time activator-inhibitor system has an interior equilibrium solution. Then, by using linear stability theory, local dynamics with different topological classifications for the interior equilibrium solution are investigated. It is investigated that for the interior equilibrium solution, discrete activator-inhibitor system undergoes Neimark-Sacker and flip bifurcations. Further chaos control is studied by the feedback control method. Finally, numerical simulations are presented to validate the obtained theoretical results.

Ionospheric anomalies through satellites can provide useful information about forthcoming earthquakes (EQs) over the epicentral regions. In this paper, we investigated seismo-ionospheric anomalies associated with the Mw 6.5 Sumatra earthquake that occurred in Indonesia on 06 December 2016 at 22:03 UT. We analyzed the total electron content (TEC) from Global Positioning System (GPS) signals received at the nearby stations around the epicenter. Furthermore, we also studied the TEC in local daytime and nighttime from Swarm satellites to confirm the EQ-induced ionospheric perturbations. The TEC showed significant perturbation within 5–10 days before the main shock in the form of positive anomalies beyond the upper bound. Similarly, Swarm satellites also validated the anomalies observed in the GPS TEC from nearby operating stations within 5–10 days over the epicentral region. The geomagnetic indices were quiet for the observed TEC anomalies within 5–10 days before the main shock, having Dst ≤ −40 nt and Kp ≤ 3. This study reveals the legitimate anomalies mainly associated with the EQ and suggests using the TEC from GPS and other satellites to look for possible future precursors with a more equipped satellite cluster.

Background: Pressure ulcers are the most common condition in bedridden patients. Almost every country is dealing with this condition instead primarily or secondary. Proper positioning and care are needed and preferred in this situation by physiotherapists and a complete home plan is given to avoid such conditions related to the disease. In accordance with this major protocol is required in hospital setups to prevent such a situation that is brutal and has increased morbidity and mortality rate. Objective: To assess knowledge and attitudes of physical therapists in different hospitals of Multan regarding pressure ulcers. Methods: : Cross-sectional design was conducted at Government and Private Hospital of Multan city and duration was from September to December 2019. 130 physical therapists that were recruited in this study were working in hospital indoors. Sample size was computed through Cochran’s formula. PUKT and SAT were used to test the knowledge and attitudes of physical therapists from government and private sector. Descriptive statistics was applied to extract result. Results: The results were deduced on the basis of satisfactory level of government and private sectors of hospitals. The statistical analysis of knowledge assessment scale “Pressure Ulcer Knowledge Test” shows maximum percentage of satisfaction i.e. 70% with minimum of 20 and maximum range of 47 with the mean value of 33.2. Our second scale “Staff Attitude Test” shows maximum participation of PTs which were 130 with minimum stats of 22 and maximum 51 with mean of 35.9. Conclusion: Knowledge and attitudes of physical therapists towards pressure ulcers in different hospitals of Multan city was found to be satisfactory. Keywords: Knowledge, Attitudes, Pressure Ulcers, Physiotherapy

In this paper, we explore the bifurcations and hybrid control in a $3\times3$ discrete-time predator-prey model in the interior of $\mathbb{R}_+^3$. It is proved that $3\times3$ model has four boundary fixed points: $P_{000}(0, 0, 0)$, $P_{0y0}\left(0, \frac{r-1}{r}, 0\right)$, $P_{0yz}\left(0, \frac{d}{f}, \frac{rf-f-dr}{cf}\right)$, $P_{x0z}\left(\frac{d}{e}, 0, \frac{a}{b}\right)$, and the unique positive fixed point: $P^+_{xyz}\left(\frac{br(d-f)+f(b+ac)}{ber}, \frac{br-b-ac}{br}, \frac{a}{b}\right)$ under certain restrictions to the involved parameters. By utilizing method of Linearization, local dynamics along with topological classifications about fixed points have been investigated. Existence of prime period and periodic points of the model are also investigated. Further for $3\times3$ model, we have explored the occurrence of possible bifurcations about each fixed point, that gives more insight about the under consideration model. It is proved that the model cannot undergo any bifurcation about $P_{000}(0, 0, 0)$ and $P_{x0z}\left(\frac{d}{e}, 0, \frac{a}{b}\right)$, but the model undergo P-D and N-S bifurcations respectively about $P_{0y0}\left(0, \frac{r-1}{r}, 0\right)$ and $P_{0yz}\left(0, \frac{d}{f}, \frac{rf-f-dr}{cf}\right)$. For the unique positive fixed point: $P^+_{xyz}\left(\frac{br(d-f)+f(b+ac)}{ber}, \frac{br-b-ac}{br}, \frac{a}{b}\right)$, we have proved the N-S as well as P-D bifurcations by explicit criterion. Further, theoretical results are verified by numerical simulations. We have also presented the bifurcation diagrams and corresponding maximum Lyapunov exponents for the $3\times3$ model. The computation of the maximum Lyapunov exponents ratify the appearance of chaotic behavior in the under consideration model. Finally, the hybrid control strategy is applied to control N-S as well as P-D bifurcations in the discrete-time model.

Abstract Spider silk is a natural polymeric fiber with high tensile strength, toughness, and has distinct thermal, optical, and biocompatible properties. The mechanical properties of spider silk are ascribed to its hierarchical structure, including primary and secondary structures of the spidroins (spider silk proteins), the nanofibril, the “core–shell”, and the “nano‐fishnet” structures. In addition, spider silk also exhibits remarkable properties regarding humidity/water response, water collection, light transmission, thermal conductance, and shape‐memory effect. This motivates researchers to prepare artificial functional fibers mimicking spider silk. In this review, the authors summarize the study of the structure and properties of natural spider silk, and the biomimetic preparation of artificial fibers from different types of molecules and polymers by taking some examples of artificial fibers exhibiting these interesting properties. In conclusion, biomimetic studies have yielded several noteworthy findings in artificial fibers with different functions, and this review aims to provide indications for biomimetic studies of functional fibers that approach and exceed the properties of natural spider silk.

The local dynamics, chaos, and bifurcations of a discrete Brusselator system are investigated. It is shown that a discrete Brusselator system has an interior fixed point P1,r if r>0. Then, by linear stability theory, local dynamical characteristics are explored at interior fixed point P1,r. Furthermore, for the discrete Brusselator system, the existence of periodic points is investigated. The existence of bifurcations around an interior fixed point is also investigated and proved that the discrete Brusselator model undergoes hopf and flip bifurcations if r,h∈ℋℬ|P1,r=r,h, h=2−r and r,h∈ℱℬ|P1,r=r,h, h=4/2−r−r2−4r, respectively. The next feedback control method is utilized to stabilize the chaos that exists in the discrete Brusselator system. Finally, obtained results are verified numerically.

Abstract We study the local dynamics and bifurcations of a two-dimensional discrete-time predator–prey model in the closed first quadrant R+2 $\mathbb{R}_{+}^{2}$. It is proved that the model has two boundary equilibria: O(0,0) $O(0,0)$, A(α1−1α1,0) $A (\frac{\alpha _{1}-1}{\alpha _{1}},0 )$ and a unique positive equilibrium B(1α2,α1α2−α1−α2α2) $B (\frac{1}{\alpha _{2}},\frac{ \alpha _{1}\alpha _{2}-\alpha _{1}-\alpha _{2}}{\alpha _{2}} )$ under some restriction to the parameter. We study the local dynamics along their topological types by imposing the method of linearization. It is proved that a fold bifurcation occurs about the boundary equilibria: O(0,0) $O(0,0)$, A(α1−1α1,0) $A (\frac{\alpha _{1}-1}{\alpha _{1}},0 )$ and a period-doubling bifurcation in a small neighborhood of the unique positive equilibrium B(1α2,α1α2−α1−α2α2) $B (\frac{1}{\alpha _{2}},\frac{\alpha _{1} \alpha _{2}-\alpha _{1}-\alpha _{2}}{\alpha _{2}} )$. It is also proved that the model undergoes a Neimark–Sacker bifurcation in a small neighborhood of the unique positive equilibrium B(1α2,α1α2−α1−α2α2) $B (\frac{1}{ \alpha _{2}},\frac{\alpha _{1}\alpha _{2}-\alpha _{1}-\alpha _{2}}{\alpha _{2}} )$ and meanwhile a stable invariant closed curve appears. From the viewpoint of biology, the stable closed curve corresponds to the periodic or quasi-periodic oscillations between predator and prey populations. Numerical simulations are presented to verify not only the theoretical results but also to exhibit the complex dynamical behavior such as the period-2, -4, -11, -13, -15 and -22 orbits. Further, we compute the maximum Lyapunov exponents and the fractal dimension numerically to justify the chaotic behaviors of the discrete-time model. Finally, the feedback control method is applied to stabilize chaos existing in the discrete-time model.

In this work, we explore the boundedness and local and global asymptotic behavior of the solutions to a second-order difference formula of the exponential type ξn+1=a+bξn−1+cξn−1e−ρξn, where a,c,ρ∈(0,∞), b∈(0,1) and the initials ξ0,ξ−1 are non-negative real numbers. Some other special cases are given. We provide two concrete numerical examples to confirm the theoretical results.

In this work, we derive the solution formulas and study their behaviors for the difference equations xn+1=αxnxn−3/−βxn−3+γxn−2,n∈ℕ0 and xn+1=αxnxn−3/βxn−3−γxn−2,n∈ℕ0 with real initials and positive parameters. We show that there exist periodic solutions for the second equation under certain conditions when β2

In this paper, we explore the global dynamical characteristics, boundedness, and rate of convergence of certain higher-order discrete systems of difference equations. More precisely, it is proved that for all involved respective parameters, discrete systems have a trivial fixed point. We have studied local and global dynamical characteristics at trivial fixed point and proved that trivial fixed point of the discrete systems is globally stable under respective definite parametric conditions. We have also studied boundedness and rate of convergence for under consideration discrete systems. Finally, theoretical results are confirmed numerically. Our findings in this paper are considerably extended and improve existing results in the literature.

In this paper, we explore local stability, attractor, periodicity character, and boundedness solutions of the second-order nonlinear difference equation. Finally, obtained results are verified numerically.

In this paper, we study the global dynamics and bifurcations of a two-dimensional discrete time host–parasitoid model with strong Allee effect. The existence of fixed points and their stability are analysed in all allowed parametric region. The bifurcation analysis shows that the model can undergo fold bifurcation and Neimark–Sacker bifurcation. As the parameters vary in a small neighbourhood of the Neimark–Sacker bifurcation condition, the unique positive fixed point changes its stability and an invariant closed circle bifurcates from the positive fixed point. From the viewpoint of biology, the invariant closed curve corresponds to the periodic or quasi-periodic oscillations between host and parasitoid populations. Furthermore, it is proved that all solutions of this model are bounded, and there exist some values of the parameters such that the model has a global attractor. These theoretical results reveal the complex dynamics of the present model.

Background: To determine the prevalence, etiological spectrum and outcomes of acute pancreatitis patients . Methods: In this was descriptive, observational, study patients presenting with clinical features of acute pancreatitis, increased serum amylase and/or lipase levels and/or CT scan abdomen with features suggestive of acute pancreatitis were included. Ranson’s scoring was done over the first 48 hours. Contrast- enhanced CT scan abdomen with pancreatic protocol was done in selected patients. Cochrane-Armitage trend test was used to determine significance of correlation between complications and severity indices. Results: Out of 154 patients 59.1% were female. Gall stones (74%) was the commonest aetiology, followed by idiopathic ( 13%). Same admission cholecystectomy was done in 44.7% of patients with gallstone pancreatitis. On admission, 14.9% of serum amylase and 18.8% (n=29) of serum lipase levels were within 3 times the upper limit of normal values. Higher Ranson’s score and modified CT severity index were associated with higher complication and mortality rates. The complication rate was 21.4 % and mortality was 7.1 % . Conclusion: Gallstone pancreatitis was found to be the most common cause. The higher rate of idiopathic pancreatitis in our study, along with higher mortality in this subgroup, could be partially explained due to lack of advanced diagnostics such as MRCP and EUS. Overall complication and mortality rate was higher for which healthcare infrastructure needs to be improved.

The importance of construction industry can not be overemphasized because it is one of the biggest contributors toward economic activities of a country. It employs a countable number of workforce and it is prone to accidents, incidents, hazards and disasters, therefore, the safety factor is equally important. The current research explores safety culture in the perspective of its important attributes. The EFQM (European Foundation for Quality Management) is taken as the bases for finding the ways and means of safety culture improvement of the construction industry. The correlation of pattern of responses is found for every attribute of the safety culture and the interrelationships and strengths are worked out to detect the involvement of the attribute.

The terrible tsunami disaster, on 26 December 2004 hit Krabi, one of the ecotourist and very fascinating provinces of southern Thailand including its various regions e.g. Phangna and Phuket by devastating the human lives, coastal communications and the financially viable activities. This research study has been aimed to generate the tsunami hazard preventing based lands use planning model using GIS (Geographical Information Systems) based on the hazard suitability analysis approach. The different triggering factors e.g. elevation, proximity to shore line, population density, mangrove, forest, stream and road have been used based on the land use zoning criteria. Those criteria have been used by using Saaty scale of importance one, of the mathematical techniques. This model has been classified according to the land suitability classification. The various techniques of GIS, namely subsetting, spatial analysis, map difference and data conversion have been used. The model has been generated with five categories such as high, moderate, low, very low and not suitable regions illustrating with their appropriate definition for the decision makers to redevelop the region.

This research study highlights two different existing and modified landslide risk algorithms for the development of landslide susceptibility models. The modified algorithm based landslide risk susceptibility model has highlighted such slope failures which possess the rate of very high velocity of the triggering at the local scale. The case study of this research is Balakot, one of the ruined city by the terrible earthquake induced landslide fissuring there in 2005. One of the previous landslide risk algorithm, developed by Varnes in 1984, was selected was modified by introducing additional parameters and criteria along with the modified landslide risk algorithm. The both algorithms entitled as mathematical models were incorporated in GIS (Geographical Information Systems) and were tested, compared and validated by the previous landslide occurred data, called as landslide inventory data. The statistical tests were applied to quantify various predicted regions in accordance of the verification of the predicted models. This comparison portrayed the significant difference in both models due to the notable difference due to significant control event parameters. It is assured that this research will help the decision makers by applying the modified algorithm based landslide susceptibility models in the field to avoid the landslide hazards for the future.

The impacts of change ever have been remained great consideration after the occurrence of natural disasters so it might be detected the expected hazard, vulnerability and risk for taking mitigative measures in future. This study has been done based on utilizing the two different date\'s satellite imageries in that context. The satellite imageries have been interpreted using the different techniques of digital image processing such as supervised classification, and post classification etc. The maximum likelihood classification scheme, based on the field visit by various latitude and longitude coordinates and the photographs of the different features using GCP (Ground Control Positioning) receiver was used. The impacts of change have been studied using change detection technique. The change study notified the different variations in the land cover and the land use set up. It is believed that this type of study in connection of occurred change due to the natural disaster in region can be very useful for developing the landslide risk, hazard and the vulnerability models which would be benefited for the decision makers in future to redevelop the regions.

The earthquake triggered enormous landslides on 8th October 2005 in the various areas of Pakistan especially in Balakot Region. This research paper fulfilled the urge to develop alternative landslide planning based on the consideration of landslide preventing measures using GIS (Geographical Informaton Systems) techniques. This specific type of land use planning differs from traditional type of land use planning due to consideration of the probable hazard of landslide disaster by applying zonation methodology for finding the appropriate suitable areas for various development purposes. The various parameters e.g. elevation, slope angle, forest/ vegetations, faults, landslide zones, and rainfall were utilized as GIS data themes in the vector format. The different GIS techniques were used: (i) Clipping the data layers; (ii) Spatial analysis by converting the vector layers into raster format; (iii) Classification of data themes into certain classes; (iv) Overlaying the data themes and (v) Map calculation techniques through GIS standard software. This applied research has found that various different regions such as high suitable, moderate suitable, low suitable and unsuitable may be considered as preventive measures from the probable hazard of the landslide disaster in future for rehabilitation and redevelopment purpose which can save human lives, residential and commercial infrastructure in future. It is believed that the various predicted regions for preventing landslide hazards can be very beneficial to the decision makers for the redevelopment of the region in future.

The landslide susceptibility models require the appropriate and reliable terrain analytical based study of the landslides prone areas using SRTM (Shuttle Radar Topography Mission) data, based on certain GIS (Geographical Information Systems) and remote sensing techniques. This research paper focuses on the analysis of the terrain conditions of Balakot region. The analytical operations have been used in the different phases: (i) Extracting the study area from the large data; (ii) preparing it into grid format; (iii) developing contour lines with certain contour intervals (iv) Re-classification of it into required classes and (v) preparation of digital terrain model with its different required various supplementary models for analyzing the terrain conditions of the study area located in Mansehra district, north part of Pakistan where the great earthquake induced landslide disaster occurred in October 2005. This analytical study has notified the different sensitive issues concerning to the critical slope angles, variation in the elevation and the surface of study area. The various distinctions in the terrain phenomenon validate the occurred and probable landslides because the topography of such study area can predict the various probable landslide hazards, vulnerability and risk threats in the region again. This analytical study can be useful for the decisive authorities by becoming pro-active to rebuild the region to mitigate the expected losses from the natural disaster.

Wireless networks perform handover to enable MS (Mobile Stations) to move from one BS (Base Station) to other BS during a session and without hiccups. Handovers are performed for many reasons such as, MS movement, varying radio conditions and capacity offloading to achieve negotiated service quality. Network congestion is generally observed at popular business places (like downtowns) and during busy hours, when load on network increases sporadically. We propose forced handover, as a load balancing technique to handle such congestion in IEEE 802.16e networks. Existing approaches like adding more channels, forming sectors, increasing channel duration and using relay stations etc. to overcome congestion are not cost effective solutions, in situations when there is episodic increase in network load; moreover such techniques are always encumbered by the modifications that involve both licensing and cost. Our strategy to cater situations of periodic congestion is to enforce BS initiated handover of MSs at cell boundaries, observing acceptable SNR (Signal to Noise Ratio) from one of the neighboring BSs with enough capacity and thereby freeing resources for MSs that cannot be switched from one cell to another (observing high SNR for being near to BS). The proposed mechanism is tested using OPNET environment using Wireless Modeler. Performance analysis validates the proposed strategy and its effectiveness to overcome such sporadic congestion is confirmed through observable improvement in traffic statistics.

The innovation of this research is the development of new model called fast moving landslide risk analysis model by modifying one of the previous prominent landslide risk algorithms focusing on the fast moving type of the landslides (such as mudslides, mud flows, block slide, rock fall and topple) based on the qualitative approach using Heuristic method in GIS (Geographical Information Systems). The different event controlling parameters and criteria were used for fast moving landslide predictive risk model. The pair wise comparison method was used in which the parameters of landslide hazard and vulnerability were compared by their assigned weights. The drawback of the used approach was justified by the standard value of consistency ratio, which proved the assigned weight of the parameters as reasonable and consistent. The model was validated by using the occurred landslides inventory data and correlation coefficient test, which showed the positive relationship between the landslide risk predicted regions and the occurred landslides locations. The various landslide events occurred on 8th October, 2005 were accumulated as landslide inventory by the interpretation of satellite imagery. The validation of the model was justified by using one of the statistical two paired, \"t\" test, and the amount of the predicted risk in the different regions. It is believed that this modified model will prove beneficial to the decision makers in future.