Analysis of the dynamics of a vector-borne infection with the effect of imperfect vaccination from a fractional perspective.

The burden of vector-borne infections is significant, particularly in low- and middle-income countries where vector populations are high and healthcare infrastructure may be inadequate. Further, studies are required to investigate the key factors of vector-borne infections to provide effective control measure. This study focuses on formulating a mathematical framework to characterize the spread of chikungunya infection in the presence of vaccines and treatments. The research is primarily dedicated to descriptive study and comprehension of dynamic behaviour of chikungunya dynamics. We use Banach's and Schaefer's fixed point theorems to investigate the existence and uniqueness of the suggested chikungunya framework resolution. Additionally, we confirm the Ulam-Hyers stability of the chikungunya system. To assess the impact of various parameters on the dynamics of chikungunya, we examine solution pathways using the Laplace-Adomian method of disintegration. Specifically, to visualise the impacts of fractional order, vaccination, bite rate and treatment computer algorithms are employed on the infection level of chikungunya. Our research identified the framework's essential input settings for managing chikungunya infection. Notably, the intensity of chikungunya infection can be reduced by lowering mosquito bite rates in the affected area. On the other hand, vaccination, memory index or fractional order, and treatment could be used as efficient controlling variables.

Modeling and analysis of the transmission of avian spirochetosis with non-singular and non-local kernel.

An acute bacterial infection called avian spirochetosis is spread by ticks to a variety of birds. Clinical symptoms can vary greatly and are frequently non-specific. To diagnose a condition, the infectious spirochete must be detected. Here, we structure an epidemic model for the transmission of avian spirochetosis to visualize the interaction between tick and bird populations. The recommended dynamics of avian spirochetosis is illustrated with the help of fractional framework. We inspected the steady-states of the system of the avian spirochetosis for the stability analysis. The next-generation technique is used to evaluate the model's reproduction parameter R0. The infection-free and endemic steady-state of avian spirochetosis were shown to be locally asymptotically stable under the specified conditions. Through mathematical skills, the positivity of solutions is determined. Additionally, evidence supporting the existence and uniqueness of the avian spirochetosis framework solution has been shown. We conduct modified simulations of the suggested avian spirochetosis system with different input factors to study the complex phenomena of avian spirochetosis under the effect of numerous input parameters. Our outcomes illustrate the significance and plausibility of fractional parameter, and they also suggest that this input parameter may adequately account for these kinds of observations.

Structural and Functional Characterization of Novel Phosphotyrosine Phosphatase Protein from Drosophila melanogaster (Pupal Retina).

A novel pair of protein tyrosine phosphatases in Drosophila melanogaster (pupal retina) has been identified. Phosphotyrosyl protein phosphatases (PTPs) are structurally diverse enzymes increasingly recognized as having a fundamental role in cellular processes including effects on metabolism, cell proliferation, and differentiation. This study presents identification of novel sequences of PTPs and their comparative homology modeling from Drosophila melanogaster (Dr-PTPs) and complexation with the potent inhibitor HEPES. The 3D structure was predicted based on sequence homology with bovine heart low molecular weight PTPs (Bh-PTPs). The sequence homologies are approximately 50% identical to each other and to low molecular weight protein tyrosine phosphatases (PTPs) in other species. Comparison of the 3D structures of Bh-PTPs and Dr-PTPs (primo-2) reveals a remarkable similarity having a four stranded central parallel ß sheet with flanking α helices on both sides, showing two right handed ß-α-ß motifs. The inhibitor shows similar binding features as seen in other PTPs. The study also highlights the key catalytic residues important for target recognition and PTPs' activation. The structure guided studies of both proteins clearly reveal a common mechanism of action and inhibitor binding at the active site and will be expected to contribute toward the basic understanding of functional association of this enzyme with other molecules.

Modeling the transmission phenomena of water-borne disease with non-singular and non-local kernel.

Drinking or recreating water that has been polluted with disease-causing organisms or pathogens is what causes waterborne infections. It should be noted that many water-borne infections can also transmit from person to person, by contact with animals or their surroundings, or by ingesting tainted food or beverages. Schistosomiasis is a water-borne infection found in different areas of the globe. Mostly people with this viral infection live in Africa with limited resources and medications. Therefore, investigation of this infection is significant to reduce its economic burden on the society. We formulated a novel epidemic model for schistosomiasis water-borne infection with the help of the Atangana-Baleanu derivative. The rudimentary theory of fractional-calculus has been presented for the analysis of our system. We start by looking at the model solution's non-negativity and uniqueness. The basic reproduction number and equilibria of the hypothesized water-borne infection model are next evaluated. Local stability of the infection-free steady-state has been established through Jacobian matrix method for R0<1. In addition, the suggested model's solution is calculated using an iterative technique. Finally, we give numerical simulations for various input values to illustrate the impact of memory index and other input factors of the system. Our findings showed the influence of input parameters on the dynamical behaviour of the schistosomiasis infection. The results demonstrate the importance and persuasive behaviour of fractional order, and reveal that fractional memory effects in the model seem to be a good fit for this type of findings.