Mathematical Theory and Modeling
https://www.iiste.org/Journals/index.php/MTM
<p><span id="internal-source-marker_0.04939836589619517"><span id="internal-source-marker_0.04939836589619517">Mathematical Theory and Modeling </span>is a peer reviewed journal published by IISTE. The journal publishes original papers at the forefront of mathematical theories, modelings, and applications. The journal is published in both printed and online versions. The online version is free access and download.</span></p><p><span>IISTE is a member of <a href="http://www.crossref.org/01company/17crossref_members.html">CrossRef</a>.</span></p><p><span><span>The DOI of the journal is: https://doi.org/10.7176/MTM</span><br /></span></p>en-USMathematical Theory and Modeling2224-5804Modeling the Survival of Stomach Cancer Patients in Meru County using The Stratified Cox Model
https://www.iiste.org/Journals/index.php/MTM/article/view/61842
<p>Cancer is a disease that can affect anyone regardless of age, social-economic status, or sex. Research has shown there are over 28,000 new cancer cases in a year in Kenya, with a mortality of 22,000, implying a 78.5% chance that the victims do not survive. If not detected early, treated on time, and the right treatment chosen, cancer treatment is less likely to succeed, reducing the chances of survival. One of the most common types of cancer is stomach cancer. It is also the most prevalent cancer in Meru County. The purpose of the study was to find the relationship between the various treatment methods and the survivorship of stomach cancer patients. By doing so, patients and health workers can select the best treatment for cancer patients at different stages. The study modeled the survival of stomach cancer patients using the Stratified Cox model in the case of Meru County, Kenya. The study's general objective was to model the survival of stomach cancer patients in Meru County using the Stratified Cox model. The data was first fitted in a Stratified Cox model to do this. Then hazard functions were determined. From the hazard functions, hazard rates were calculated using R version 4.3.1. Chemotherapy was used as a reference category. The study used secondary data obtained from Meru General Hospital between 2017 and 2021. Different treatment methods: radiotherapy, chemotherapy, hormone therapy, and surgery are compared for each stage while considering several demographic characteristics such as age and sex. The research investigated the hazard rates that, in turn, helped find the survival of patients with stomach cancer based on the treatment method used. Hazard ratios were obtained from the collected data to determine and recommend the best treatment method at a particular stage of stomach cancer. After analysis, results showed that surgery is the best treatment for stage 1 and 2 cancer, while radiotherapy and chemotherapy are the best for stage 3 and 4, respectively. Notably, patients below 50 have higher survival rates than those above 50. It was also noted that women have higher survival rates than men. The three objectives were met, where the first objective involved fitting the data into the model. Hazard functions were formed, and the hazard rates were calculated using the coefficients from the hazard functions. Based on the objectives, it was recommended that modeling data after combining several treatments should be done. Also, the survivorship of patients after combining treatments should be found and compared with the survivorship after using one treatment at a time. Lastly, since herbal treatment is becoming a common treatment, enough data should be corrected and the treatment compared with other treatment methods.</p> <p><strong>Keywords</strong><em>: </em>Stomach Cancer, Stratified Cox model, Hazard ratio/rates, chemotherapy, radiotherapy, hormone therapy, surgery</p>Kelvin Wanjohi NyawiraRobert Gitunga MuriungiJacob Oketch Okungu13Modelling Divorce Epidemic on Network
https://www.iiste.org/Journals/index.php/MTM/article/view/61843
<p>Most couples entering into marriage are happy and do not anticipate divorce as an option. However, in reality, marriage is complicated, and many factors can lead to divorce. Using a compartmental model, we simulated and analyzed transmission network of divorce spread in continuous time on networks (that is, we analyzed married- divorced-separated model on networks). According to our findings, divorced individuals or nodes can cause many marriage nodes to become separated. Again there were few divorced nodes at the peak and at the end of the epidemic, but most marriages resulted in separation at the end of the epidemic. At the end of the epidemic, 80% of married nodes became separated nodes, which is a very serious problem. This suggests that divorce or separation is contagious and can spread quickly through indirect contact. This makes it vital to examine the effect of divorce to the population so as reduce the number of broken homes at the end of the divorce epidemic.</p> <p><strong>Keywords: </strong>compartmental model, complex systems, Marriage networks, divorce epidemics</p>Patience Pokuaa GambrahAbdul-Samad Abdul-Rahaman13Modelling the impact of insecurity on human existence and agricultural activities
https://www.iiste.org/Journals/index.php/MTM/article/view/61844
<p>Food constitutes one of the basic necessities of life and the availability of food supply to all and sundry provides the pedestals upon which human security is defined. In addition, the general quest for global development and advancement are often crippled in a society governed by food scarcity or insecurity. The cases of food and nutritional insecurity seems to be a worldwide challenge calling for urgent interventions, especially in this advent of banditry and herdsmen-farmers conflicts, a devastating state with enormous negative impacts on both human lives and the environs. This paper uses the concept of dynamical systems to derive a mathematical model that evaluates the impact of herdsmen/bandits attacks on the lives of farmers and their agricultural activities. The analytical outcome of the model is supplemented with numerical simulations using MATLAB mathematical applications. The results show that there exist significance influence of the exposure rate of the susceptible and the sponsoring of herdsmen attacks by some elites on the lives of farmers and the low engagement in agricultural activities. In addition, the number of migrants (including those that escape the nest of herdsmen with or without injury) increases in search for treatment and/or safety in nearby communities. The analysis of some of the model parameters also provided useful information about the system dynamics leading to possible measures in curtailing insecurity for harmonious living among herdsmen and farmers.</p> <p><strong>Keywords:</strong><strong> </strong>Modelling, Agriculture, Herdsmen, Insecurity, Dynamical systems, Analysis<strong></strong></p>Grace O. Agaba13Some Properties on Skew Polynomials Ring
https://www.iiste.org/Journals/index.php/MTM/article/view/61845
<p><span>Derivatives in polynomials were first defined by Ore. Since then, it has been used to construct many things, such as skew polynomials code with derivatives, constructed by Suprijanto and Tang in 2021. In that paper, the skew polynomial ring is defined explicitly.............</span></p><p><strong>Keywords: </strong>ring, automorphism, derivatives, skew-polynomials ring, construction</p><p> </p><p><span><strong>More details can be found in the full paper.</strong></span></p>Muhammad Irfan HidayatMei Dita KumalaIntan Muchtadi-Alamsyah13