ABSTRACT. In this paper, we suggest a biomathematical numerical method for analysing mRNA nucleotides sequences based on UA/CG Fibonacci numbers proportions. This method is used to evaluate then compare the spike genes related to the main SARS-CoV2 VARIANTS currently circulating within the world population. The 10 main results proposed to be reproduced by peers are: 1/ SARS-CoV2 genome and spike evolution in one year 2020-2021. 2/ SARS-CoV2 Origins. 3/ Comparing 11 reference variants spikes. 4/ analysing 32 CAL.20C California variant patients spikes. 5/ Toward a meta mRNA Fibonacci gene end message code. 6/ Analysing S501 UK, S484 South Africa and « 2 mutations » INDIA variants. 7/ Suggesting a possible variants spike mRNA palindrome symmetry metastructure improving mRNA stability then infectiousness. 8/ Analysing Fibonacci Metastructures in the mRNA coding for the vaccines PFIZER and MODERNA. 9/ Does the CG-rich modification of the synonymous codons of the spikes of the 2 mRNA vaccines affect the expression and quantity of SARS-CoV2 antibodies? 10/ The exceptional case of the Brazilian variant P.1. Particularly, we suggest the following conjecture at mRNA folding level : CONJECTURE of SARS-CoV2 VARIANTS: The growth of long Fibonacci structures in the shape of "podiums" for almost all of the variants studied (UK, California, South Africa, India, etc.) suggests the probable folding of the Spike mRNA in the form of a "hairpin", which can strengthen the cohesion and the lifespan of this mRNA. Finally, we show that these kinds of Fibonacci matastructures disapear TOTALLY by analysing the published mRNA sequences of PFIZER and MODERNA vaccines. One fact is certain, the two mRNAs of the Moderna and Pfizer vaccines will result in a low functionality of the spike vaccine. This is because their designers by seeking greater stability, have doped to build CG rich sequences which, as soon as they are inserted into the human host, will, paradoxically, seek to mutate, like SARS-CoV2 variants, towards CG ==> UA forms in order to improve their STABILITY and LIFETIME. We conclude using new biomathematics theoretical methods (Master code and numerical standing waves), and comparing the Spikes of the two vaccines Moderna and Pfizer, that there will be very probable differences in stability and shelf life of the two respective mRNAs vaccines. However, “State of the Art” analyzes will disclose that their two protein sequences are strictly identical. By modified their synonymous codons using different strategies, no one can guarantee that the quantity of antibodies generated will be identical in the two cases. We wish to draw attention to the great ADAPTATION power - at the global scale of their genomes - of the most infectious VARIANTS, such as the BRAZIL 20J / 501Y.V3 variant (P.1). This is very worrying for the VACCINES <==> VARIANTS run: We demonstrate how the Brazilian variant P.1 which becomes uncontrollable in Brazil in April 2021 has a level of organization of long metastructures of 17,711 bases covering the genome which is 3.6 more important than that of the 2 reference genomes SARS-CoV2 and worldwide D614G. We suggest that this high level of overall structure of this variant contributes to the stability of this genome and, might explain its greater contagiousness.

In (Venetz et al., 2019), authors rebuilt the essential genome of Caulobacter crescentus through the process of chemical synthesis rewriting and studied the genetic information content at the level of its essential genes. Then, they reduced the native Caulobacter crescentus native Caulobacter NA1000 genome sequence real genome ( 4042929 bp ) to the 785,701-bp reduced synthetic genome. Here we demonstrate the existence of a palindromic-like mirror structure that exists in real genomes and disappears totally in the synthetic genome. This biomathematic meta-organization is based on characteristic proportions of Fibonacci numbers between DNA single strand nucleotides proportions TC / AG on the one hand and TG / AC on the other hand. In both cases, we suggest that this meta-structure enhances the three-dimensional cohesion of the two DNA strands of the genome. We then generalize this study to the different synthetic genomes and synthetic cells published by the Craig Venter Institute on Mycoplasma Mycoides JCVI-syn1.0 (in 2010), JCVI-syn3.0 (in 2016) and JCVI-syn3A (in 2019). Finally, in the discussion section, we extend this study to synthetic genomes of E-Coli and Yeast chromosome XII.

ABSTRACT. In this paper, we run for all INDIA mutations and variants a biomathematical numerical method for analysing mRNA nucleotides sequences based on UA/CG Fibonacci numbers proportions (Perez, 2021). In this study, we limit ourselves to the analysis of whole genomes, all coming from the mutations and variants of SARS-CoV2 sequenced in India in 2020 and 2021. We then demonstrate - both on actual genomes of patients and on variants combining the most frequent mutations to the SARS-CoV2 Wuhan genomes and then to the B.1.617 variant - that the numerical Fibonacci AU / CG metastructures increase considerably in all cases analyzed in ratios of up to 8 times. We can affirm that this property contributes to a greater stability and lifespan of messenger RNAs, therefore, possibly also to a greater INFECTUOSITY of these variant genomes. Out of a total of 108 genomes analyzed: - None ("NONE") of them contained a number of metastructures LOWER than those of the reference SARS-CoV2 Wuhan genome. - Eleven (11) among them contained the same number of metastructures as the reference genome. - 97 of them contained a GREATER number of metastructures than the reference genome, ie 89.81% of cases. The average increase in the number of metastructures for the 97 cases studied is 4.35 times the number of SARS-CoV2 UA/CG 17711 Fibonacci metastructures. Finally, we put a focus on B.1.617.2 crucial exponential growth Indian variant. Then, we demonstrate, by analyzing the main worldwide 19 variants, both at the level of spikes and of whole genomes, how and why these UA / CG metastuctures increase overall in the variants compared to the 2 reference strains SARS-CoV2 Wuhan and D614G.

This paper explores the critical role of biomathematics in cancer research, focusing on how mathematical models enhance our understanding of tumor growth and optimize treatment strategies. It begins with an overview of cancer biology, highlighting the complexities of tumor dynamics and the molecular mechanisms driving growth. The paper then delves into various mathematical modeling approaches, including deterministic, stochastic, and agent-based models, illustrating their applications in predicting tumor behavior and treatment responses. Case studies demonstrate the real-world impact of these models on optimizing chemotherapy, radiation therapy, and immunotherapy. Challenges such as data availability, model complexity, and clinical translation are discussed, alongside future directions in the field, including advances in computational power and personalized medicine. Ultimately, this research emphasizes the transformative potential of biomathematics in improving cancer treatment outcomes and underscores the importance of interdisciplinary collaboration in advancing the field.

The Benford method can be used to detect manipulation of epidemiological or trial data during the validation of new drugs. We extend here the Benford method after having detected particular properties for the Fibonacci values 1, 2, 3, 5 and 8 of the first decimal of 10 runs of official epidemiological data published in France and Italy (positive cases, intensive care, and deaths) for the periods of March 1 to May 30, 2020 and 2021, each with 91 raw data. This new method – called “BFP” for Benford-Fibonacci-Perez - is positive in all 10 cases (i.e. 910 values) with an average of favorable cases close to 80%, which, in our opinion, would validate the reliability of these basic data.

Forest resources are renewable,rational exploitation and utilization of forest resources are not only conducive to sustainable development of population, but also can obtain higher economic benefits. Based on actual timber harvesting problems,a combined harvesting model of timber and non-timber with nonlinear harvesting term was established.Firstly, using the qualitative theory of ordinary differential equations, the dynamic behavior of the model is studied, and the existence and stability of the equilibrium point of the model are proved .Secondly, the optimal control solution is obtained by using the optimal control theory.Finally, the optimal harvesting strategy of timber and non-timber products is given based on the numerical simulation results, which provides a certain theoretical basis for the sustainable development of forestry ecological economy.

This study explores the intersection of bioinformatics, computational biology, and biomathematics, focusing on how mathematical models are applied to analyze biological data and develop computational tools. This study highlights the foundational role of biomathematics in biological research including genomics, proteomics, and systems biology. Key areas of focus include the use of statistical models, algorithms, and simulations to create computational tools to aid in data interpretation and drug discovery. Additionally, this paper delves into emerging trends such as artificial intelligence, machine learning, and big data in bioinformatics. By analyzing case studies and real-world applications, this study underscores the significance of biomathematics in advancing biological sciences and the potential for future innovations in personalized medicine and interdisciplinary approaches.

This study investigates the application of fractal geometry to the analysis of vertebrate respiratory systems, focusing on the branching patterns of the bronchial tree across diverse species. Using a combination of mathematical modeling and computational visualization, we explore how fractal dimensions and branching characteristics reflect evolutionary adaptations to various habitats and physiological demands. The research encompasses a range of vertebrates, including humans, horses, dolphins, chickens, iguanas, and bullfrogs, representing diverse taxonomic groups and ecological niches. Our analysis reveals a clear gradient of complexity in respiratory structures, correlating strongly with metabolic rates and environmental adaptations. Mammals, particularly those adapted for high-performance activities like horses, demonstrate the most complex fractal patterns, indicating highly efficient gas exchange systems. In contrast, ectothermic species such as iguanas and bullfrogs exhibit simpler structures, reflecting their lower metabolic demands and alternative respiratory strategies. The study employs fractal dimension calculations, L-system modeling, and lacunarity analysis to quantify and visualize these differences. Our findings suggest that fractal analysis provides valuable insights into the relationship between form and function in vertebrate respiratory systems, offering a novel perspective on comparative physiology and evolutionary biology. This research not only enhances our understanding of respiratory system evolution but also has potential applications in biomimetic design, medical diagnostics, and ecological physiology. It demonstrates the power of interdisciplinary approaches, combining advanced mathematics with biological principles to uncover fundamental patterns in nature.