Mashih Ibn Yasin Adan

Malaria remains a major global public health challenge, with a substantial burden of morbidity and mortality concentrated in sub-Saharan Africa and other tropical and subtropical regions. The complex transmission process involving Plasmodium parasites, Anopheles mosquito vectors, and human hosts makes mathematical modeling an important tool for understanding transmission dynamics and evaluating control strategies. This review provides a comprehensive synthesis of mathematical modeling approaches for malaria transmission and control, including deterministic compartmental models, stochastic models, optimal control frameworks, spatial models, and cost-effectiveness analyses. Particular attention is given to major intervention strategies, including vector control, vaccination, antimalarial treatment, and other integrated control approaches. The review also examines the effects of seasonality, climate variability, drug and insecticide resistance, spatial heterogeneity, and human movement on malaria transmission and intervention outcomes. A bibliography-based keyword frequency analysis and word-cloud visualization are used to identify dominant research themes, followed by a comparative assessment of modeling approaches and intervention strategies. The findings highlight the importance of integrating multiple interventions with context-specific epidemiological and environmental conditions. Overall, mathematical models provide valuable support for optimizing malaria control strategies and addressing important challenges toward malaria elimination.

Nipah virus (NiV) is a zoonotic pathogen with a high case fatality rate, posing a significant and ongoing threat to public health in Asia. This study develops a comprehensive mathematical framework to analyze its transmission dynamics and evaluate effective control strategies. We introduce a novel six-compartment model (SEAIHR) that stratifies the population into Susceptible, Exposed, Asymptomatic, Symptomatic Infected, Hospitalized, and Recovered individuals, incorporating key features such as waning immunity. Analytical results determine the basic reproduction number and establish the global stability of both the disease-free and disease equilibria, confirming a forward bifurcation at the epidemic threshold. A sensitivity analysis identifies the recruitment rate and the disease transmission rate as the most influential parameters on outbreak potential. Furthermore, we formulate an optimal control problem to evaluate the impact of three time-dependent intervention measures: public health campaigns to reduce contact, isolation of symptomatic individuals, and improved treatment for hospitalized patients. The optimal strategies derived from Pontryagin’s Maximum Principle demonstrate a significant reduction in the overall infection burden and intervention costs. Numerical simulations validate the model and show that these combined controls can effectively minimize the final epidemic size while increasing the population’s immunity. This work provides a quantitative framework to guide the design of efficient public health policies for managing and mitigating Nipah virus outbreaks.

The study investigates the intricate interactions, particularly the antagonistic dynamics, between two entities inhabiting a nonhomogeneous circumstance subjected to harvesting pressures. We initiate our analysis by constructing a robust mathematical framework utilizing partial differential equations (PDEs) to model the behaviors of the two species. We rigorously demonstrate the substantiality and exclusivity of solutions to the formulated model. In this context, we establish pivotal conditions that facilitate species coexistence, as well as delineate scenarios wherein one species may exert competitive pressures sufficient to drive the other towards extinction. Additionally, we identify conditions that could culminate in the simultaneous extinction of both species. The findings yield a comprehensive relative analysis of two distinct harvesting levels, providing critical insights into their differential impacts on species dynamics. Furthermore, we substantiate our theoretical conclusions through a series of numerical simulations, which serve to validate our model and its implications. J. Bangladesh Math. Soc. 45.1 (2025) 32–49

Besides maintaining health precautions, vaccination has been the only prevention from SARS-CoV-2, though no clinically proved 100% effective vaccine has been developed till date. At this stage, to withhold the debris of this pandemic-experts need to know the impact of the vaccine efficacy rates, the threshold level of vaccine effectiveness and how long this pandemic may extent with vaccines that have different efficacy rates. In this article, a mathematical model study has been done on the importance of vaccination and vaccine efficiency rate during an ongoing pandemic. We simulated a five compartment mathematical model to analyze the pandemic scenario in both California, and whole U.S. We considered four vaccines, Pfizer (95%), Moderna (94%), AstraZeneca (79%), and Johnson & Johnson (72%), which are being used rigorously to control the SARS-CoV-2 pandemic, in addition with two special cases: a vaccine with 100% efficacy rate and no vaccine under use. SARS-CoV-2 related data of California, and U.S. were used in this study. Both the infection and death rates are very high in California. Our model suggests that the pandemic situation in California will be under control in the last quartile of the year 2023 if vaccination program is continued with the Pfizer vaccine. During this time, six waves may happen from the beginning of the immunization where the case fatality and recovery rates will be 1.697% and 98.30%, respectively. However, according to the considered model, this period might be extended to the mid of 2024 when vaccines with lower efficacy rates are used. On the other hand, the daily cases and deaths in the U.S. will be under control at the end of 2026 with multiple waves. Although the number of susceptible people will fall down to none in the beginning of 2027, there is less chance to stop the vaccination program if vaccinated with a vaccine other than a 100% effective vaccine or Pfizer, and at that case vaccination program must run till the mid of 2028. According to this study, the unconfirmed-infectious and infected cases will be under control at the end of 2027 and at the mid of 2028, respectively. The more effective a vaccine is, the less people suffer from this malign infection. Vaccines which are less than 90% effective do not have notable contribution to control the pandemic besides hard immunity. Furthermore, specific groups of people are getting prioritized initially, mass vaccination and quick responses are required to control the spread of this disease.