Biomathematics

Magnetohydrodynamic peristaltic flow of Jeffery fluid in an asymmetric channel is addressed. The channel walls satisfy the convective conditions. Asymmetry here is considered due to wave trains of different amplitudes and phases. Solutions for the velocity, temperature and pressure gradient are obtained using long wavelength approximation. Plots reflecting the impact of various parameters of interest are shown and examined.

"""Lyapunov functions for some mathematical models of ecological commensalism between two species are introduced. Global stability of the unique positive equilibrium is thereby established.

Keyword: Models of ecological commensalism; Lyapunov's asymptotic stability theorem; Global stability"""

Nowadays, in addition to traditional qualitative methods, quantitative techniques are also a standard tool to describe biological systems behavior. An example is the broad class of mathematical models, based on differential equations, used in ecology, biochemical kinetics, epidemiology, gene regulatory networks, etc. Independent of their simplicity or complexity, all these models have in common (generally unknown a priori) parameters that need to be identified from observations (data) of the real system, usually available on the literature, obtained by specific assays or surveyed by public health offices. Before using this data to calibrate the models, a good practice is to judge the most influential parameters. That can be done with aid of the Sobol’ indices, a variance-based statistical technique for global sensitivity analysis, which measures the individual importance of each parameter, as well as their joint-effect, on the model output (a.k.a. quantity of interest). These variance-based indexes may be computed using Monte Carlo simulation but, depending on the model, this task can be very costly. An alternative approach for this scenario is the use of surrogate models to speed-up the calculations. Using simple biological models, from different areas, we develop a tutorial that illustrates how practitioners can use Sobol’ indices to quantify, in a probabilistic manner, the relevance of the parameters of their models. This tutorial describes a very robust framework to compute Sobol’ indices employing a polynomial chaos surrogate model constructed with the UQLab package.

This paper presents a seven-dimensional ordinary differential equation modelling the transmission of Plasmodium falciparum malaria between humans and mosquitoes with non-linear forces of infection in form of saturated incidence rates. These incidence rates produce antibodies in response to the presence of parasite-causing malaria in both human and mosquito populations.The existence of region where the model is epidemiologically feasible is established. Stability analysis of the disease-free equilibrium is investigated via the threshold parameter (reproduction number R0) obtained using the next generation matrix technique. The model results show that the disease-free equilibrium is asymptotically stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. The existence of the unique endemic equilibrium is also determined under certain conditions. Numerical simulations are carried out to confirm the analytic results and explore the possible behavior of the formulated model.

كان الهدف من البحث: التعرف على فاعلية وحدة مقترحة في الرياضيات البيولوجية في تنمية مهارات الفهم العميق لدى طلاب المرحلة الثانوية، و قد تحددت مشكلة البحث في السؤال الرئيس الآتي: "ما فاعلية وحدة مقترحة في الرياضيات البيولوجية في تنمية التحصيل ومهارات الفهم العميق لدى طلاب الصف الثاني الثانوي الشعبة العلمية تخصص العلوم"؟ ويتفرع من هذا السؤال الرئيس الأسئلة الفرعية التالية:
1. ما موضوعات الرياضيات البيولوجية التي يجب توافرها لإعداد وحدة مقترحة في "الرياضيات البيولوجية" لطلاب الصف الثاني الثانوي الشعبة العلمية تخصص العلوم؟
2. ما مهارات الفهم العميق اللازم تنميتها لدى طلاب الصف الثاني الثانوي الشعبة العلمية تخصص العلوم؟
3. ما صورة وحدة مقترحة في الرياضيات البيولوجية لطلاب الصف الثاني الثانوي الشعبة العلمية تخصص العلوم؟
4. ما فاعلية الوحدة المقترحة في رفع مستويات التحصيل لبلوم (المعرفة، الفهم، التطبيق، التحليل، التركيب) لدى طلاب الصف الثاني الثانوي الشعبة العلمية تخصص العلوم؟
5. ما فاعلية الوحدة المقترحة في تنمية مهارات الفهم العميق (مهارات التفكير التوليدي"الطلاقة، والمرونة، ووضع الفرضيات، والتنبؤ في ضوء المعطيات، ومهارة إتخاذ القرار، ومهارة التفسير، ومهارات طرح الاسئلة) لدى طلاب الصف الثاني الثانوي الشعبة العلمية تخصص العلوم؟
وقام الباحثان بإعداد أدوات البحث التالية :
أعد الباحثان قائمة بموضوعات الرياضيات البيولوجية التي يجب تنميتها لدى طلاب المرحلة الثانوية، وكذلك قائمة بمهارات الفهم العميق اللازم تنميتها لدى طلاب المرحلة الثانوية والتي على ضوئهما تم إعداد تصور لوحدة مقترحة بعنوان (الرياضيات البيولوجية) لتنمية التحصيل في الرياضيات البيولوجية ومهارات الفهم العميق لدى طلاب الصف الثاني الثانوي العلمي ، وإعداد دليل للمعلم للوحدة المقترحة، وقام الباحثان بإعداد اختبار تحصيلي، واختبار لمهارات الفهم العميق، وتم تدريس الوحدة المقترحة لمجموعة البحث بلغ عدد الطلاب (35 طالباَ) من طلاب الصف الثاني الثانوي العلمي قسم العلوم من مدرسة سيدي سالم الثانوية بمحافظة كفر الشيخ. في الفصل الدراسي الأول في العام الدراسي 2014 / 2015 .
وتم تطبيق الاختبار التحصيلي، واختبار مهارات الفهم العميق قبل تدريس الوحدة وبعد الانتهاء من التدريس لمجموعة البحث، وكان من أهم نتائج البحث وجود فرق دال إحصائياً بين متوسطي درجات مجموعة البحث من طلاب الصف الثاني الثانوي في التطبيقين القبلي والبعدي لصالح التطبيق البعدي لمجموعة البحث وذلك في كل من : الاختبار التحصيلي، واختبار مهارات الفهم العميق عند مستوى 0.05 .
وكان من أهم التوصيات : استخدام وحدة الرياضيات البيولوجية بالشعب العلمية بالمرحلة الثانوية لتنمية مهارات الفهم العميق. وتدريب الطلاب المعلمين بكليات التربية علي تدريس محتوى تكاملي بين الرياضيات والبيولوجي. وتدريب معلمي الأحياء أتناء الخدمة لتمكينهم من اكتساب مهارات تدريس محتوى علمي تكاملي بين الرياضيات والبيولوجي. وتزويد معلمي الأحياء بدليل معلم لتدريس وحدة الرياضيات البيولوجية. وتضمين مناهج الأحياء بالمرحلة الثانوية بمحتوى رياضياتي.

A mathematical model of malaria dynamics with naturally acquired transient immunity in the presence of protected travellers is presented. The qualitative analysis carried out on the autonomous model reveals the existence of backward bifurcation, where the locally asymptotically stable malaria-free and malaria-present equi-libria coexist as the basic reproduction number crosses unity. The increased fraction of protected travellers is shown to reduce the basic reproduction number significantly. Particularly, optimal control theory is used to analyse the non-autonomous model, which incorporates four control variables. The existence result for the optimal control quadruple, which minimizes malaria infection and costs of implementation, is explicitly proved. Effects of combining at least any three of the control variables on the malaria dynamics are illustrated. Furthermore, the cost-effectiveness analysis is carried out to reveal the most cost-effective strategy that could be implemented to prevent and control the spread of malaria with limited resources.

A deterministic compartmental model for the transmission dynamics of malaria incorporating vigilant human compartment is studied. The model is qualitatively analyzed to investigate its asymptotic behavior with respect to the equilibria. It is shown, using a linear Lyapunov function, that the disease-free equilibrium is globally asymptotically stable when the associated basic reproduction number is less than unity. When the basic reproduction number is greater than the unity, under certain specifications on the model parameters, we prove the existence of a globally asymptotically stable endemic equilibrium with the aid of a suitable nonlinear Lyapunov function.

We formulate and analyze Zika virus transmission model with three nonlinear forces of infection from infected mosquito, asymptomatic and symptomatic humans. The sensitivity indexes of the associated parameters of the model with respect to the basic reproduction number are calculated to identify intervention strategies for prevention and control of Zika virus. Multiple time-dependent optimal controls are considered. The analysis based on the use of optimal control theory made popular by Pontryagin's maximum principle is carried out, and the resulting optimality system is quantitatively simulated to investigate the impact of the controls on the dynamics of Zika virus. In addition, the effects of non-linearity of the forces of infection and other key parameters on the disease transmission are illustrated.

—A deterministic epidemiological model describing the spread of infectious disease characterized by pseudo-recovery due to incomplete treatment is studied. The resulting SEIRI model in a closed system is robustly analysed. Trans-critical bifurcation at the threshold, R0 = 1, is investigated and the global asymptotic dynamics of the model around the disease-free and endemic equilibria are explored by the aid of suitable Lyapunov functionals. Further, sensitivity analysis complemented by simulations are performed to determine how changes in parameters affect the dynamical behaviour of the system.

ABSTRAK. Pada artikel ini dikonstruksi model matematika penyebaran penyakit menular tipe SEIT (Susceptible Exposed Infective Treatment). Adanya variasi virus dan kondisi jasmani yang berbeda tiap individu serta adanya perubahan perilaku dari individu rentan menjadi alasan pembentukan model dengan perbedaan periode laten dan tingkat kejadian tersaturasi. Dari hasil analisis dinamik, model memiliki dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit yang bersifat stabil saat bilangan reproduksi dasar bernilai lebih kecil atau sama dengan satu, dan titik kesetimbangan endemi yang eksis dan bersifat stabil saat bilangan reproduksi dasar bernilai lebih besar dari satu.Hasil analisis dinamik diilustrasikan dengan simulasi numerik menggunakan software Matlab.

ABSTRACT. In this paper, a SEIT (Susceptible Exposed Infective Treatment) mathematical model ofthe spread ofinfectious diseases is constructed. The virus variation, differentphysical conditions of each individual, and behavioral change of susceptible individual sare the reason to forma model with differences in latent period and saturated incidence rate. From dynamical analysis results, the model has two equilibrium points, i.e. the disease-free equilibrium point which stable whenthe basic reproduction numberis less than orequal to one, and the endemic equilibrium point which exiss and stable when the basic reproduction numberis greatert han one. The results of dynamical analysis is illustrated by numerical simulation using Matlab software.

"This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems:

1) How the activity of neurons, via synaptic changes, can shape the topology of the network they form part of, and

2) How the resulting network structure, in its turn, might condition aspects of brain behaviour.

Although the emphasis is on neural networks, several theoretical findings which are relevant for complex networks in general are presented - such as a method for studying network evolution as a stochastic process, or a theory that allows for ensembles of correlated networks, and sets of dynamical elements thereon, to be treated mathematically and computationally in a model-independent manner. Some of the results are used to explain experimental data - certain properties of brain tissue, the spontaneous emergence of correlations in
all kinds of networks... - and predictions regarding statistical aspects of the central nervous system are made. The mechanism of Cluster Reverberation is proposed to account for the near-instant storage of novel information the brain is capable of."

To better understand the dynamics of the hepatitis B virus (HBV) infection, we introduce an improved HBV model with standard incidence function, cytotoxic T lymphocytes (CTL) immune response, and take into account the effect of the export of precursor CTL cells from the thymus and the role of cytolytic and noncytolytic mechanisms. The local stability of the disease-free equilibrium and the chronic infection equilibrium is obtained via characteristic equations. Furthermore, the global stability of both equilibria is established by using two techniques, the direct Lyapunov method for the disease-free equilibrium and the geometrical approach for the chronic infection equilibrium.

Farmers frequently decide where to locate the colonies of their domesticated eusocial bees, especially given the following mutually exclusive scenarios: (1) there are limited nectar and pollen sources within the vicinity of the apiary that cause competition among foragers; and (2) there are fewer pollinators compared to the number of inflorescence that may lead to suboptimal pollination of crops. We hypothesize that optimally distributing the beehives in the apiary can help address the two scenarios stated above. In this paper, we develop quantitative models (specifically using linear programming) for addressing the two given scenarios. We formulate models involving the following factors: (1) fuzzy preference of the beekeeper; (2) number of available colonies; (3) unknown-but-bounded strength of colonies; (4) probabilistic carrying capacity of the plant clusters; and (5) spatial orientation of the apiary.

Modelagem matemática de câncer/tumor: seria o mais novo aliado na luta contra o câncer/tumor? Nas últimas décadas, tem havido um aumento significativo no diagnóstico (precoce) de câncer em todo o mundo. Segundo o INCA (Instituto Nacional de Câncer), os casos de câncer ficaram somente atrás de doenças cardiovasculares como motivo de óbitos em 2008. Esse aumento de diagnósticos de câncer pode ser associado em parte ao desenvolvimento de novas tecnologias, como imagens em 3D da área de interesse. De forma similar, tem havido um aumento na incidência de câncer, em muitos casos com origens desconhecidas, outras como resultado de fatores já conhecidos como exposição excessiva às radiações solares. Tratamentos de câncer variam muito no que tange os procedimentos de abordagem, como exemplo: termoterapia, imunoterapia, radioterapia, quimioterapia entre outros, como estratégias híbridas. Igualmente, o custo desses tratamentos variam consideravelmente (um tratamento de imunoterapia pode chegar à 80.000 por pessoa por aplicação). Não obstante todos os avanços no diagnóstico, monitoramento e tratamento do câncer, muitas questões ainda não foram respondidas, sendo objeto de pesquisas/financiamentos em vários países. Dois acontecimentos não correlacionados em 2019 mostram um termômetros bem ativos no brasil na questão de modelagem computacional de câncer nos últimos anos, para possíveis aplicações em medicina. Em 2019, um grupo responsável pela modelagem de câncer da Fiocruz do Rio de Janeiro ganhou um edital da Faperj para modelagem de câncer, de outro lado um grupo do LNCC (Laboratório Nacional de Computação Científica) organizou um evento sobre modelagem de câncer, que vem acontecendo com certa periodicidade, na sua quinta edição. Nesse evento, titulado V Encontro em Modelagem Matemática do Crescimento Tumoral, foi possível ver a diversidade de modelos atualmente sendo foco de pesquisas em grupos espalhados pelo Brasil. Basicamente, quase todos os tipos de câncer, e achados, estão sendo encapsulados em modelos, o que do ponto de vista de pesquisa mostra um termômetro bem ativo. O mais interessante de se mencionar desses modelos é a inclusão de achados recentes, como da epigenética e imunoterapia. De outros eventos anteriores em outras instituições, como em 2014 em Trento, Itália, titulado Mathematical Models and Methods for Living Systems, foi possível ver tanto a diversidade desses modelos em seção dedicada somente à modelagem matemático-computacional de câncer quanto a complexidade e nível de detalhes tendo o foco do modelo como guia. Atualmente, ocorreu uma mudança de paradigma em resposta a estudos em biologia sistêmica, biologia molecular, e teoria de redes complexas: não se foca mais no silenciamento de um gene em particular dito como responsável pelo câncer como pensava a "biologia do câncer tradicional", agora se ataca redes, que são consideradas responsáveis pelo câncer; sendo o gene algo substituído pelo conceito de hub (um gene relacionado ao câncer com alto nível de interações com outros genes). Isso é necessário devido aos achados nas últimas décadas de que genes trabalham em redes, essas redes são chamadas de 'redes de regulação gênica'. Essas redes são modeladas empregando-se teoria de grafos; a mesma teoria usada por estudiosos em redes de internet, redes sociais, entre outros exemplos do dia a dia. A consequência direta desses achados reside em tratamentos mais eficientes, com menos efeitos colaterais, uma vez que o alvo é a rede. A questão que se pode colocar é, mas não respondida aqui: até onde esses modelos ajudarão no entendimento do câncer? Hoje falam-se de vacinas para câncer, de cura e outras notícias que circulam pelo mundo científico. Seria possível fazer uso desses modelos para testar novos fármacos e/ou novas terapias? Modelagem de câncer estar dentro de uma área bem maior, que é a modelagem de sistemas biológicos (que em essência é a exploração de modelos matemáticos e computacionais para estudar sistemas biológicos). Câncer, devido à sua complexidade e importância dentro da comunidade médica, tem recebido muita atenção da comunidade científica nas últimas décadas, em especial da indústria farmacêutica. Uma das possíveis contribuições dos modelos seria a redução do custo tanto físico quando financeiro dos testes de medicamentos/terapias. Entre desafios da modelagem matemática de câncer, sempre apontados em eventos científicos, é a indústria farmacêuticas: modelos baseados em redes complexas e teoria de sistemas

Controle de peso é um vultoso desafio para qualquer pessoa. Ordinariamente, apreensão com relação a controle de peso abrolha tanto devido a fatores estéticos como de bem-estar. Umas das maiores problemáticas jaz na ocorrência de que o processo de alimentar e controle interno de energia, chamado cientificamente de homeostase, é alcançado de forma automática pelo corpo, em um processo análogo a "tecnologia da informação", que integra diferentes partes do corpo, como sistema digestivo e cérebro; obtém-se escasso controle desse do ponto de vista global. Neste artigo, disserta-se sobre o conceito de biomatemática, um exemplo, emprestado de uma pesquisa recente em desenvolvimento, é explorado para nortear o leitor em torno do conceito de biomatemática. O desígnio do artigo é chamar a apreciação para a crescente pendência por profissionais em áreas que unam engenharias, física, matemática e ciências da vida. Mesmo que essa demanda já existe por um bom tempo, de modo recente, isso se tem mostrado mais proeminente. Simulações computacionais, acompanhadas de um modelo matemático emprestado e adaptado da literatura, é discernido. O artigo é concluído com algumas altercações, exposições finais, e as atinente referências; as referências foram selecionadas de modo a servir como um quadro sinóptico para interessados nas discussões.

Immersi nella spiaggia cosmica, trasportati da un piccolo granello di polvere, non abbiamo mai smesso di interrogarci sulla nostra origine. La natura della vita sulla terra e la ricerca della vita altrove nell’universo convergono ad un'unica sfida: la ricerca di ciò che siamo. “Dalla semplicità alla complessità” è una sfida che mi sono posto, ossia il provare a trattare un argomento complesso, non inquadrato in una singola disciplina scientifica, ma attuale grazie alle sempre più raffinate applicazioni computazionali. La scienza della complessità tratta argomenti come il problema degli n-corpi della meccanica celeste (ossia un sistema che descrive le interazioni di più di due corpi liberi di muoversi sotto l’azione della forza gravitazionale reciproca), la ricerca della soluzione analitica delle equazioni di Navier-Stokes dalla fluidodinamica e così via… Il filo generale sul quale si basa questo lavoro è la complessità dal punto di vista matematico, biologico e sociale, come si vedrà vi sono gerarchie via via emergenti e quella sociale non è un punto d’arrivo, ma fa parte di una continua evoluzione.

In the last decades Exp-function method has been used for solving fractional differential equations. In this paper, we obtain exact solutions of fractional generalized reaction Duffing model and nonlinear fractional diffusion–reaction equation. The fractional derivatives are described in the modified Riemann–Liouville sense. The fractional complex transform has been suggested to convert fractional-order differential equations with modified Riemann–Liouville derivatives into integer-order differential equations, and the reduced equations can be solved by symbolic computation.

For university biology students transferring ‘mathematics’ to a life science discipline is as uncomfortable for them as being in a mathematics class. I say ‘uncomfortable’ as about 50% of our life science students tend to adopt a rigid stance when required to take their raw data and generate data suitable for their assignments. It is unlikely that my students are innumerate, rather this statement of not being able to “do maths” represents a reluctance on the part of these students to participate in activities that, to them, look like maths.

In this paper, we explain why the chaotic mutation (CM) model of J. M. Bahi and C. Michel (2008) simulates the genes mutations over time with good accuracy. It is firstly shown that the CM model is a truly chaotic one, as it is defined by Devaney. Then, it is established that mutations occurring in genes mutations have indeed a same chaotic dynamic, thus making relevant the use of chaotic models for genomes evolution. Transposition and inversion dynamics are finally investigated.

This paper offers some backgrounding on the sometimes vexed area of 'academic identities' through descriptions and reflections of select moments in my career where my scholarly work was informed by my home discipline of Biology and extended into other discipline spaces, specifically the Arts. I offer examples of my work where the "A" in STEAM is evident including examples of poetry and visual art projects that have allowed for the communication of ideas without the constraints of scientific prose. I reflect on the importance (to me) of working across disciplines as fields of practice and of connecting with others like me within science (including students), and across and outside of science and so offering validation. These Science-Art moments have given me permission to be myself, to exhale.

In this article, the pattern learned from the classic or conventional rotating circular genetic code is transferred to a 64-grid model. In this non-static representation, the codons for the same amino acid within each quadrant could be exchanged, wobbling or rotating in a quantic way similar to the electrons within an atomic orbit. Represented in this 64-grid format are the three rules of variation encompassing 4, 2, or 1 quadrant, respectively: 1) same position in four quadrants for the essential hydrophobic amino acids that have U at the center, 2) same or contiguous position for the same or related amino acids in two quadrants, and 3) equivalent amino acids within one quadrant. Also represented is the mathematical balance of the odd and even codons, and the most used codons per amino acid in humans compared to one diametrically opposed organism: the plant Arabidopsis thaliana, a comparison that depicts the difference in third nucleotide preferences: a C/U exchange for 11 amino acids, a G/A exchange for 2 amino acids, and G/U or C/A exchanges for one amino acid, respectively; by studying these codon usage preferences per amino acid we present our two hypotheses: 1) A slower translation in vertebrates and 2) a faster translation in invertebrates, possibly due to the aqueous environments where they live. These codon usage preferences may also be able to determine genomic compatibility by comparing individual mRNAs and their functional third dimensional structure, transport and translation within cells and organisms. These observations are aimed to the design of bioinformatics computational tools to compare human genomes and to determine the exchange between compatible codons and amino acids, to preserve and/or to bring back extinct biodiversity, and for the early detection of incompatible changes that lead to genetic diseases.