Radiative Microwave Heating of Hyperthermia Therapy on Breast Cancer in a Porous Medium

Cancer is a leading cause of morbidity and mortality worldwide, yet much is still unknown about its mechanism of establishment and destruction. Recently, studies had shown that tumor cells cannot survive under the high temperature conditions. This treatment technique is called Hyperthermia. This report presents the case of radiative microwave heating of hyperthermia therapy on breast cancer in a porous medium. In this study, the steady state is solved analytically while unsteady state is solved using semi-implicit finite difference to get a more accurate prediction of blood temperature distributions within the breast tissues. A moderate temperature hyperthermia treatment is apply which results into cell death due to an increase in the level of cell sensitivity to radiation therapy and blood flow in tumor and oxygen. The results show that by applying metabolic heat generation rate of 3.97X105Wm−3, it takes upto 2 minutes for the tumor cells to get the require therapeutic temperature poin

Dynamic model of COVID-19 disease with exploratory data analysis

Novel Coronavirus is a highly infectious disease, with over one million confirmed cases and thousands of deaths recorded. The disease has become pandemic, affecting almost all nations of the world, and has caused enormous economic, social and psychological burden on countries. Hygiene and educational campaign programmes have been identified to be potent public health interventions that can curtail the spread of the highly infectious disease. In order to verify this claim quantitatively, we propose and analyze a nonlinear mathematical model to investigate the effect of healthy sanitation and awareness on the transmission dynamics of Coronavirus disease (COVID-19) prevalence. Rigorous stability analysis of the model equilibrium points was performed to ascertain the basic reproduction number R 0 , a threshold that determines whether or not a disease dies out of the population. Our model assumes that education on the disease transmission and prevention induce behavioral changes in individuals to imbibe good hygiene, thereby reducing the basic reproduction number and disease burden. Numerical simulations are carried out using real life data to support the analytic results.http://www.elsevier.com/locate/sciafam2021Mathematics and Applied Mathematic

Mathematical model for the estrogen paradox in breast cancer treatment

Estrogen is known to stimulate the growth of breast cancer, but is also effective in treating the disease. This is referred to as the“estrogen paradox”. Furthermore, short-term treatment with estrogen can successfully eliminate breast cancer, whereas long-term treatment can cause cancer recurrence. Studies highlighted clinical correlations between estrogen and the protein p53 which plays a pivotal role in breast cancer suppression. We sought to investigate how the interplay between estrogen and p53 impacts the dynamics of breast cancer, and further explore if this could be a plausible explanation for the estrogen paradox and the paradoxical tumor recurrence that results from prolonged treatment with estrogen. For this, we propose a novel ODE based mathematical model that accounts for dormant and active cancer cells, along with the estrogen hormone and the p53 protein. We analyze the model’s global stability behavior using the Poincaré-Bendixson theorem and results from differential inequalities. We also perform a bifurcation analysis and carry out numerical simulations that elucidate the roles of estrogen and p53 in the estrogen paradox and its long term estrogen paradoxical effect. The mathematical and numerical analyses suggest that the apparent paradoxical role of estrogen could be the result of an interplay between estrogen and p53, and provide explicit conditions under which the paradoxical effect of long-term treatment may be prevented.The DST/NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering at the University of Pretoria and the Center of Excellence in Mathematical and Statistical Sciences (DST-NRF COE-MaSS), South Africa.https://link.springer.com/journal/2852023-03-03hj2023Mathematics and Applied Mathematic

Optimal Control Analysis of a Mathematical Model for Breast Cancer

In this paper, a mathematical model of breast cancer governed by a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet is discussed. Several comprehensive mathematical analyses were carried out using a variety of analytical methods to study the stability of the breast cancer model. Also, sufficient conditions on parameter values to ensure cancer persistence in the absence of anti-cancer drugs, ketogenic diet, and cancer emission when anti-cancer drugs, immune-booster, and ketogenic diet are included were established. Furthermore, optimal control theory is applied to discover the optimal drug adjustment as an input control of the system therapies in order to minimize the number of cancerous cells by considering different controlled combinations of administering the chemotherapy agent and ketogenic diet using the popular Pontryagin’s maximum principle. Numerical simulations are presented to validate our theoretical results

Qualitative Analysis of a Dengue Fever Model

In this paper, a deterministic mathematical model of the Dengue virus with a nonlinear incidence function in a population is presented and rigorously analysed. The model incorporates control measures at the aquatic and adult stages of the vector (mosquito). The stability of the system is analysed for the disease-free equilibrium and the existence of endemic equilibria under certain conditions. The local stability of the Dengue-free equilibrium is investigated via the threshold parameter (reproduction number) that was obtained using the next-generation matrix techniques. The Routh–Hurwitz criterion, along with Descartes’ rule of signs change, established the local asymptotically stability of the model whenever R0<1 and was unstable otherwise. The comparison theorem was used to establish the global asymptomatically stability of the model

Mathematical modeling of malaria disease with control strategy

This article suggested and analyzed the transmission dynamics of malaria disease in a population using a nonlinear mathematical model. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. Moreso, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The optimal control problem was formulated using Pontryagin’s maximum principle, and three control strategies: disease prevention through bed nets, treatment and insecticides were incorporated. The optimality system was stimulated using an iterative technique of forward-backward Runge-Kutta fourth order scheme, so that the impacts of the control strategies on the infected individuals in the population can be determined. The possible influence of exploring a single control, the combination of two, and the three controls on the spread of the disease was also investigated. Numerical simulation was carried out and pertinent findings are displayed graphically.The Institutional Research Fund of University of Zululand; Mathematical and Statistical Sciences in South Africa and the support of DSI-NRF Centre of Excellence in Mathematical & Statistical Sciences (CoE-MaSS) for the postdoc position at University of Pretoria, South Africa.http://scik.org/index.php/cmbnam2020Mathematics and Applied Mathematic