Let X(t) be the number of tumor cells at time t, and Pr{X(t) = n} = pn(t) is the density of X. A “birth”, i.e., an increase of one of the total population of cancer cells, can occur either by mutation of a normal cell caused by the action of the carcinogen, consisting of randomly (Poisson) distributed hits, or by reproduction of existing cancer cells. A death of a tumor cell occurs as an additive combination of non-immunological and immunological elements. Once a tumor is initiated by carcinogenic action, it undergoes a birth and death process with infinitesimal birth rate linear and infinitesimal death rate composed of a linear and a nonlinear term, the former due to non-immunological deaths, the latter to immunological feedback. The death rate per tumor cell due to immunological response is proportional to the total number of antigen-producing (tumor) cells; thus, the total death rate is quadratic. Although this assumes a very simple mechanism for the action of immunological feedback, it is nevertheless a first step.

The Mathematical Model

ed/Indexed in Applied Mechanics Reviews, Aquatic Sciences and Fisheries Abstracts part 2 (ASFA-2), Compendex, CSA Illumina, Current

Shock and Vibration

In this paper, we establish daily confirmed infected cases prediction models for the time series data of America by applying both the long short-term memory (LSTM) and extreme gradient boosting (XGBoost) algorithms, and employ four performance parameters as MAE, MSE, RMSE, and MAPE to evaluate the effect of model fitting. LSTM is applied to reliably estimate accuracy due to the long-term attribute and diversity of COVID-19 epidemic data. Using XGBoost model, we conduct a sensitivity analysis to determine the robustness of predictive model to parameter features. Our results reveal that achieving a reduction in the contact rate between susceptible and infected individuals by isolated the uninfected individuals, can effectively reduce the number of daily confirmed cases. By combining the restrictive social distancing and contact tracing, the elimination of ongoing COVID-19 pandemic is possible. Our predictions are based on real time series data with reasonable assumptions, whereas the accurate course of epidemic heavily depends on how and when quarantine, isolation and precautionary measures are enforced.

Time series prediction of COVID-19 transmission in America using LSTM and XGBoost algorithms

Biology and mathematics are key lessons in our curriculum from elementary to high school. Biology science studies the structure and evolution of living organisms and is directly linked to human life on the planet. Many of us have been wondering, "Why do we learn Math?" And "Where will they serve us?" In this work, by linking the courses of Biology and Mathematics, we highlight the role and value of mathematical science in analyzing and explaining real-world situations and phenomena. The experiment we conducted in three classrooms of our school, enabled us to mathematical modeling of infectious diseases, to draw conclusions, to motivate us to further research mathematical models and simulations that would interpret real-world conditions and contemporary ones. Therefore, it will help in making decisions and preventive measures.

/pdf/mathematical-modeling-of-the-epidemic-diseases-3qekcaq7oe.pdf

Mathematical modeling of the epidemic diseases

Effects of binary hybrid nanofluid on heat transfer and fluid flow in a triangular-corrugated channel: An experimental and numerical study

In this study, we examined various forms of mathematical models that are relevant for the containment, risk analysis, and features of COVID-19. Greater emphasis was laid on the extension of the Susceptible-Infectious-Recovered (SIR) models for policy relevance in the time of COVID-19. These mathematical models play a significant role in the understanding of COVID-19 transmission mechanisms, structures, and features. Considering that the disease has spread sporadically around the world, causing large scale socioeconomic disruption unwitnessed in contemporary ages since World War II, researchers, stakeholders, government, and the society at large are actively engaged in finding ways to reduce the rate of infection until a cure or vaccination procedure is established. We advanced argument for the various forms of the mathematical model of epidemics and highlighted their relevance in the containment of COVID-19 at the present time. Mathematical models address the need for understanding the transmission dynamics and other significant factors of the disease that would aid policymakers to make accurate decisions and reduce the rate of transmission of the disease.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/pa.2306

Mathematical modeling for infectious viral disease: The COVID-19 perspective.

This paper investigates the effects of thermal radiation and variable viscosity flow down along an inclined plane with boundary conditions at free surface. The major problem includes internal heat generation, increase or decrease in temperature, and other thermo physical properties. The thermo physical properties include Grashf number, Nusselt number, Viscosity and Solar radiation parameter. The problems created have not been examined. Thus, this work examined the effect of temperature and velocity profiles on the various values of coefficient of viscosity, also the effects of solar radiation parameter on the major property of the fluid flow down along an inclined plane. The partial differential equations for the problem are continuity, momentum and energy equations. These are nonlinear dimensionless equations governing the fluid flow down the inclined plane using integration method. The equations for the fluid flow, temperature and velocity of the problem are reduced to their final forms using perturbation method. Analytical expressions are employed to obtain the value of the velocity and temperature profiles in terms of parameters under the considerations in the flow field. The parameters are the major factors influencing the properties of the fluid flow down along an inclined plane. Hence, the viscosity of the fluid increases as the velocity of the fluid decreases while increase in the solar radiation parameter increases velocity of the fluid. Also the quantities of radiant energy absorbed by the fluid flow bring changes in the temperature of the fluid. Increase in Nusselt decreases the velocity of the fluid. Grashof number increases while the temperature of the fluid also decreases. In conclusion, viscosity of the fluid decreases with an increase in temperature due to cohesion and molecular momentum exchange between fluid layer and the parameters are found to have a significant effect over the velocity and temperature profiles of the fluid flow down an inclined plane at free surface. It will also useful for the industries in the production of the various fluids (liquid or gas) such as vegetable oil, palm oil and steam generation along an inclined plane and so on. © 2019 TJES, College of Engineering, Tikrit University DOI: http://dx.doi.org/10.25130/tjes.27.3.03 ةصلاخلا ققحتو هذه ةقرولا يف راثآ عاعشلإا يرارحلا قفدتو ةجوزللا ةريغتملا ىلإ لفسلأا ىلع لوط ىوتسم لئام عم فورظ ةيدودح ىلع حطس رح . لمشتو ةلكشملا ةيسيئرلا ديلوت ةرارحلا ةيلخادلا ، ةدايزو ةجرد ةرارحلا وأ اهضفخ ، ريغو كلذ نم صئاصخلا فلا يزي ةيئا ةيرارحلا . لمشتو صاوخلا ةيئايزيفلا ةيرارحلا مقر Grashof ، مقرو Nusselt ، لماعو ةجوزللا عاعشلإاو يسمشلا . ملو ثحبت لكاشملا ةئشانلا . يلاتلابو ، نإف اذه لمعلا سرد ريثأت ةجرد ةرارحلا و ةعرس تاحمل نع فلتخم ميق لماعم ةجوزللا اضيأ راثآ عاعشلإا يسمشلا ملعملا ة ىلع تاكلتمملا ةيسيئرلا نم لئاوسلا قفدتت ىلع لوط ردحنملا . تلاداعملا ةيلضافتلا ةيئزجلا ةلكشملل يه ةيرارمتسلاا مخزلاو تلاداعمو ةقاطلا . هذه تلاداعم لاب داعبأ ريغ ةيطخ مكحت قفدت لئاسلا لفسأ ىوتسملا ليمملا مادختساب ةقيرط لماكتلا . تلاداعم قفدت لئاوسلا ةجردو حلا رار ة ةعرسو ةلكشملا متي اهضيفخت ىلإ اهلاكشأ ةيئاهنلا مادختساب ةقيرط تابارطضلاا . مدختستو * Corresponding author: E-mail : usmanma@yahoo.com Mustapha M.A. Usman, Sefiu S.A. Onitilo, Titilope S.T. Moshood / Tikrit Journal of Engineering Sciences (2020) 27(3): 12-24... 13 تاريبعتلا ةيليلحتلا لوصحلل ىلع ةميق حملام ةعرسلا ةجردو ةرارحلا نم ثيح تارتمارابلا يف راطإ تارابتعلاا يف لاجم قفدتلا . تارتمارابلا يه لماوعلا ةيسيئرلا يتلا رثؤت ىلع صئاصخ قفدت لئاسلا ىلإ لفسأ ىلع لوط ىوتسم لئام يلاتلابو ، نإف ةجوزل لئاسلا دادزت عم ضافخنا ةعرس لئاسلا يف نيح نأ ةدايزلا يف لماعم عاعشلإا يسمشلا ديزت ةعرس لئاسلا . امك نأ تايمك ةقاطلا ةعشملا يتلا اهصتمي قفدت لئاوسلا ثدحت تاريغت يف ةجرد ةرارح لئاسلا . ةدايزلا يف ( ون يس تل ) للقت نم ةعرس لئاسلا ديزي ددع فوشارجلا امنيب ضفخنت ةجرد ةرارح لئاسلا يف ماتخلا ةجوزل لئاوسلا صقانتي عم ةدايز يف ةجرد ةرارحلا ببسب كسامتلا ةيئيزجلا مخز لدابتلا نيب لئاسلا ةقبط تاملعملا تدجو نأ نوكي اهل ريثأت ريبك ىلع ةعرس و ةجرد ةرارحلا تاحمل نم ئاوسلا ل قفدتت ةرئاطلا ليمت ىلع حطسلا . امك هنأ نوكيس اديفم تاعانصلل يف جاتنإ لئاوسلا ةفلتخملا ( لئاسلا وأ زاغلا ) لثم تيزلا يتابنلا تيزو ليخنلا ديلوتو راخبلا ىلع لوط ىوتسم لئام امو ىلإ كلذ

/pdf/the-effect-of-thermal-radiation-and-variable-viscosity-4e0p6bdg13.pdf

The Effect of Thermal Radiation and Variable Viscosity Parameters on a Fluid Flow Down Along an Inclined Plane With Free Surface

In this paper, the effects of hematocrit of red blood cells on blood flow through a stenosed human carotid artery was considered by taking blood as a Newtonian fluid. The governing equations on blood flow were derived. The mathematical content involved in the equations are the variables of interest such as number of stenosis , percentage of hematocrit  of red blood cells in the blood, flow rate, wall shear stress, and viscosity of the blood. Guided by medical data collected on the constraint of blood flow in stenosed human carotid arteries, the governing equations were used to check the effects of pressure gradient, wall shear stress, velocity, and volumetric flow rate of blood in the human carotid arteries. Also, the one-dimensional equation for the steady and axially symmetric flow of blood through an artery was transformed using Einsteinâ€™s coefficient of viscosity and hematocrit of red blood cells with the help of the boundary conditions. The effects of hematocrit on the blood flow characteristics are shown graphically and discussed briefly. It was discovered that the resistance increases as the level of hematocrit increases. Also, the wall shear stress decreases with the increase in the hematocrit level of the red blood cells.

/pdf/effects-of-hematocrit-on-blood-flow-through-a-stenosed-human-3holqzi3rd.pdf

Effects of Hematocrit on Blood Flow Through A Stenosed Human Carotid Artery

This paper studies the combined effect of a transverse magnetic field and internal heat generation on the flow of an incompressible third-grade fluid through parallel plates of uniform temperature. Analytical solutions of the dimensionless nonlinear ordinary differential equations are obtained using regular perturbation method implemented on a symbolic package-Mathematica. Variations of flow pa- rameters on the velocity and temperature profiles are presented and discussed.

https://www.acadpubl.eu/ap/sites/default/files/201400802005.pdf

Heat generating hydromagnetic third grade fluid flow through isothermal plates with ohmic heating effect

In this study, the response of two homogeneous parallel beams with two-parameter Pasternak elastic foundation subjected to a constant uniform partially distributed moving force is considered. On the basis of Euler-Bernoulli beam theory, the fourth order partial differential equations of motion describing the behavior of the beams when subjected to a moving force were formulated. In order to solve the resulting initial-boundary value problem, finite Fourier sine integral technique and differential transform scheme were employed to obtain the analytical solution. The dynamic responses of the two beams obtained was investigated under moving force conditions using MATLAB. The effects of speed of the moving force, layer parameters such as stiffness (K_0) and shear modulus (G_0 ) have been conducted for the moving force. Various values of speed of the moving load, stiffness parameters and shear modulus were considered. The results obtained indicates that response amplitudes of both the upper and lower beams increases with increase in the speed of the moving load. Increasing the stiffness parameter is observed to cause a decrease in the response amplitudes of the beams. The response amplitudes decreases with increase in the shear modulus of the linear elastic layer.

/pdf/forced-response-vibration-of-simply-supported-beams-with-an-2i3iyahymd.pdf

S. A. Onitilo

Papers

Mathematical modeling for infectious viral disease: The COVID-19 perspective.

The Effect of Thermal Radiation and Variable Viscosity Parameters on a Fluid Flow Down Along an Inclined Plane With Free Surface

Effects of Hematocrit on Blood Flow Through A Stenosed Human Carotid Artery

Heat generating hydromagnetic third grade fluid flow through isothermal plates with ohmic heating effect

Forced response vibration of simply supported beams with an elastic pasternak foundation under a distributed moving load