Mathematical modeling and stability analysis of the novel fractional model in the Caputo derivative operator: A case study.

The fundamental goal of this research is to suggest a novel mathematical operator for modeling visceral leishmaniasis, specifically the Caputo fractional-order derivative. By utilizing the Fractional Euler Method, we were able to simulate the dynamics of the fractional visceral leishmaniasis model, evaluate the stability of the equilibrium point, and devise a treatment strategy for the disease. The endemic and disease-free equilibrium points are studied as symmetrical components of the proposed dynamical model, together with their stabilities. It was shown that the fractional calculus model was more accurate in representing the situation under investigation than the classical framework at α = 0.99 and α = 0.98. We provide justification for the usage of fractional models in mathematical modeling by comparing results to real-world data and finding that the new fractional formalism more accurately mimics reality than did the classical framework. Additional research in the future into the fractional model and the impact of vaccinations and medications is necessary to discover the most effective methods of disease control.

Perturbations in the T cell receptor ß repertoire during malaria infection in children: A preliminary study.

The changes occurring in the T cell repertoire during clinical malaria infection in children remain unknown. In this study, we undertook the first detailed comparative study of the T cell repertoire in African children with and without clinical malaria to test the hypothesis that clonotypic expansions that occur during P. falciparum infection will contribute to the generation of a T cell repertoire that is unique to each disease state. We profiled the complementarity-determining region 3 (CDR3) of the TCRß chain sequences from children with Plasmodium falciparum infections (asymptomatic, uncomplicated and severe malaria) and compared these with sequences from healthy children. Interestingly, we discovered that children with symptomatic malaria have a lower TCR diversity and frequency of shared (or "public") TCR sequences compared to asymptomatic children. Also, TCR diversity was inversely associated with parasitemia. Furthermore, by clustering TCR sequences based on their predicted antigen specificities, we identified a specificity cluster, with a 4-mer amino acid motif, that is overrepresented in the asymptomatic group compared to the diseased groups. Further investigations into this finding may help in delineating important antigenic targets for vaccine and therapeutic development. The results show that the T cell repertoire in children is altered during malaria, suggesting that exposure to P. falciparum antigens disrupts the adaptive immune response, which is an underlying feature of the disease.

Predicting Antigenicity of Influenza A Viruses Using biophysical ideas.

Antigenic variations of influenza A viruses are induced by genomic mutation in their trans-membrane protein HA1, eliciting viral escape from neutralization by antibodies generated in prior infections or vaccinations. Prediction of antigenic relationships among influenza viruses is useful for designing (or updating the existing) influenza vaccines, provides important insights into the evolutionary mechanisms underpinning viral antigenic variations, and helps to understand viral epidemiology. In this study, we present a simple and physically interpretable model that can predict antigenic relationships among influenza A viruses, based on biophysical ideas, using both genomic amino acid sequences and experimental antigenic data. We demonstrate the applicability of the model using a benchmark dataset of four subtypes of influenza A (H1N1, H3N2, H5N1, and H9N2) viruses and report on its performance profiles. Additionally, analysis of the model's parameters confirms several observations that are consistent with the findings of other previous studies, for which we provide plausible explanations.

Trans-Allelic Model for Prediction of Peptide:MHC-II Interactions.

Major histocompatibility complex class two (MHC-II) molecules are trans-membrane proteins and key components of the cellular immune system. Upon recognition of foreign peptides expressed on the MHC-II binding groove, CD4+ T cells mount an immune response against invading pathogens. Therefore, mechanistic identification and knowledge of physicochemical features that govern interactions between peptides and MHC-II molecules is useful for the design of effective epitope-based vaccines, as well as for understanding of immune responses. In this article, we present a comprehensive trans-allelic prediction model, a generalized version of our previous biophysical model, that can predict peptide interactions for all three human MHC-II loci (HLA-DR, HLA-DP, and HLA-DQ), using both peptide sequence data and structural information of MHC-II molecules. The advantage of this approach over other machine learning models is that it offers a simple and plausible physical explanation for peptide-MHC-II interactions. We train the model using a benchmark experimental dataset and measure its predictive performance using novel data. Despite its relative simplicity, we find that the model has comparable performance to the state-of-the-art method, the NetMHCIIpan method. Focusing on the physical basis of peptide-MHC binding, we find support for previous theoretical predictions about the contributions of certain binding pockets to the binding energy. In addition, we find that binding pocket P5 of HLA-DP, which was not previously considered as a primary anchor, does make strong contribution to the binding energy. Together, the results indicate that our model can serve as a useful complement to alternative approaches to predicting peptide-MHC interactions.