Seasonal variability and stochastic branching process in malaria outbreak probability.

BACKGROUND: Malaria is the world's most fatal and challenging parasitic disease, caused by the Plasmodium parasite, which is transmitted to humans by the bites of infected female mosquitoes. Bangladesh is the most vulnerable region to spread malaria because of its geographic position. In this paper, we have considered the dynamics of vector-host models and observed the stochastic behavior. This study elaborates on the seasonal variability and calculates the probability of disease outbreaks. METHODS: We present a model for malaria disease transmission and develop its corresponding continuous-time Markov chain (CTMC) representation. The proposed vector-host models illustrate the malaria transmission model along with sensitivity analysis. The deterministic model with CTMC curves is depicted to show the randomness in real scenarios. Sequentially, we expand these studies to a time-varying stochastic vector-host model that incorporates seasonal variability. Phase plane analysis is conducted to explore the characteristics of the disease, examine interactions among various compartments, and evaluate the impact of key parameters. The branching process approximation is developed for the corresponding vector-host model to calculate the probability outbreak. Numerous numerical results are accomplished to observe the analytical investigation. RESULTS: Seasonality and contact patterns affect the dynamics of disease outbreaks. The numerical illustration provides that the probability of a disease outbreak depends on the infected host or vector. Additionally, periodic transmission rates have a great influence on the probability outbreak. The basic reproduction number (R0) is derived, which is the main justification for studying the dynamical behavior of epidemic models. CONCLUSIONS: Seasonal variability significantly impacts malaria transmission, and the probability of disease outbreaks is influenced by time and the initial number of infected individuals. Moreover, the branching process approximation is applicable when the population size is large enough and the basic reproduction number is less than 1. In the future, such analysis can help decision-makers understand the impact of various parameters and their stochastic behavior in the vector-host model to prevent such types of disease outbreaks.

Factors affecting success and failure in higher education mathematics: Students' and teachers' perspectives.

Background: Students from Bangladesh pursuing STEM education often encounter obstacles when tackling diverse mathematical problems within various educational settings. Frequently, they find themselves lacking the essential prerequisite knowledge and strong foundational skills necessary to engage with the teaching and learning resources utilized at the undergraduate level, resulting in a significant number of students needing to seek readmission annually. Objective: The objective of this study is to explore the determinants of academic achievement among university undergraduates majoring in mathematics in Bangladesh. Employing a mixed-method research approach, the study combines quantitative and qualitative data analysis to examine the viewpoints of both students and educators concerning these factors. The authors primarily emphasize classifying the factors that impact the efficacy of mathematics pedagogical methods. Methodology: The study is structured into three phases: i. An initial exploratory qualitative survey. ii. A quantitative triangulation survey. iii. Followed by explanatory semi-structured interviews. Findings: To begin, the initial qualitative survey identified significant factors that contribute to students' achievements and setbacks in mathematics. Subsequently, the quantitative analysis verified both similarities and distinctions in the perspectives of students and educators. Furthermore, the correlation coefficient analysis revealed that male students frequently exhibit inconsistency and a lack of enthusiasm for studying, resulting in subpar performance. Conversely, female students frequently cited challenges like the difficulty of connecting mathematical theories to real-world applications, heavy course loads, and limited resources as reasons for their academic difficulties. Lastly, insights from interviews with students highlighted their acknowledgment of inadequate study practices, excessive reliance on memorization, suboptimal teaching methods, low motivation, and external distractions as key factors leading to their struggles. They also recognized the importance of consistent practice, a solid comprehension of concepts, regular study routines, and effective learning strategies for successful mathematics education. In contrast, educators emphasized the significance of students having clear concepts, natural aptitude, motivation, and a sense of curiosity as pivotal elements for successful learning in mathematics. Conclusion: This conclusion suggests a new beginning in the realm of local mathematics pedagogy, achieved by scrutinizing teacher-student feedback about the factors influencing success and failure, considering the diverse individual and contextual variables at play. To foster mutual trust and understanding between students and teachers, it may be beneficial to engage in open discussions and interactions.