Table of Content
Mathematical model
Open AccessArticleMathematical Model and Analysis of Measles Dynamics in a Population with Limited Resources
Kenneth Ojotogba Achema
Annals of Communications in Mathematics 2025,
8 (1),
116-127
DOI: https://doi.org/10.62072/acm.2025.080109
AbstractThis study explores the mathematical modelling of measles transmission dy- namics in Nigeria, with a specific focus on assessing the impact of a single-dose vaccina- tion strategy. Given the resurgence of measles outbreaks, especially in regions with low vaccination coverage, this research aims to develop a robust model that can simulate dis- ease transmission and evaluate vaccination strategies. The primary objective of the study is to understand how varying levels of vaccination coverage, vaccine efficacy, and immunity waning affect the disease dynamics. A modified SEIR (Susceptible-Exposed-Infectious- Recovered) model was used, incorporating additional compartments for individuals vac- cinated with one dose, as well as a factor for immunity waning. Data from Nigeria’s Measles Situation Report (April 2024) informed the parameter values, initial population distributions, and vaccination rates within the model, providing a real-world context. The study employed numerical simulations using MATLAB to analyse the effects of vaccina- tion rates, immunity waning, and other epidemiological parameters on measles transmis- sion. The results reveal that high vaccination coverage specifically, achieving coverage rates above 80% with the single-dose strategy significantly reduces the disease prevalence, indicating effective outbreak prevention. However, the simulations also show that im- munity waning can increase susceptibility, suggesting a potential need for booster dose to sustain long-term immunity in the population. It recommends that public health authorities prioritize reaching at least 90% vaccination coverage with two doses and consider booster doses if immunity waning proves significant. These insights provide a foundation for en- hancing measles control efforts, informing policy decisions, and guiding future research on infectious disease dynamics in Nigeria and similar settings.
Open AccessArticleMathematical model formulation and analysis of the transmission dynamics of Lassa fever
W.T. Ademosu, K.O. Achema* and D. J. Yayaha
Annals of Communications in Mathematics 2026,
9(1),
9
DOI: https://doi.org/10.62072/acm.2026.09009
Abstract. In 1969, two missionary nurses died due to Lassa fever infection, which led to the identification of the Lassa virus (LASV) in Nigeria. Infections from the Lassa virus are about 80% asymptomatic, but severe cases normally result in multi-organ failure or death. This accounts for about 15% of the hospitalized cases. Different scientific strategies to eradicate the disease have yielded minimal results. In this study, a mathematical model to study the transmission dynamics of Lassa fever is formulated and analyzed. The model has five compartments. The human population is compartmentalized into three sub-populations, while the rodent population is compartmentalized into two sub-populations. The model has two equilibrium states, namely, the disease-free equilibrium (DFE) and the disease endemic equilibrium (DEE). The stability analysis of the DFE revealed that it is locally asymptotically stable when the basic reproduction number (R0) is less than one and unstable otherwise. The sensitivity analysis on the model reproduction number revealed that the infection transmission rates from human-to-human, rodent-to-human, and from human-to-rodent are the causes of the disease persistence in the human population. The Hopf-bifurcation analysis of the model using the transmission rate from both rodents and humans to humans as the bifurcation parameter shows the stability point of the model at αh = 0.025. The numerical analysis result perfectly aligns with the model’s qualitative results obtained.