Table of Content
reproduction number
Open AccessArticleA Spatial Nonlinear Mathematical Model of Malaria Transmission Dynamics Using Vector Control Strategies
Charity Jumai Alhassan and Kenneth Ojotogba Achema*
Annals of Communications in Mathematics 2024,
7 (3),
205-240
DOI: https://doi.org/10.62072/acm.2024.070301
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.
Open AccessArticleMathematical model formulation and analysis of the transmission dynamics of Lassa fever
D. J. Yayaha, W.T. Ademosu and K.O. Achema*
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.