Annals of Communications in Mathematics

AbstractMalaria is one of the serious life-threatening diseases with negative effects on both the social and economic aspects of human life. Researching into its curtailment or eradication is necessary for elevating human health and social-economic status. In thisregard, this study focuses on the spatial non-linear mathematical model to investigate how vector control strategies are correlated with the dynamics of malaria transmission. The study employs a non-linear partial differential equations (NPDE) mathematical model to investigate malaria transmission. The model system incorporates human (host), mosquito (vector), and invasive alien plant populations. Some applicable epidemiological mathematical analyses were carried out on the model system, such as critical points, stability, the basic reproduction number, local asymptotic stability (LAS), bifurcation, global as- ymptotic stability (GAS), wave speed, and numerical analyses using relevant data were extensively analysed. Using the sharp threshold conditions imposed on the basic reproduction number, we were able to show that the model exhibited the backward bifurcation phenomenon and the DFE was shown to be globally asymptotic stable (GAS) under certain conditions. It was found that the invasive alien plants have significant effects on malaria transmission. This study suggests that mosquito repellent plants should be planted around the human environment to replace the invasive plants so as to reduce mosquito shelters andfeeding opportunities for mosquitoes.

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.