Document Type : Research Article
Authors
1
Department of Mathematics, Joseph Sarwuan Tarka University, Makurdi, Benue State, Nigeria.
2
Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia.
3
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India.
4
Department of Family Medicine, Federal University Teaching Hospital Lafia, Nasarawa State, Nigeria.
5
Department of Family Medicine, Faculty of Clinical Sciences, Federal University Lafia, Nasarawa State, Nigeria.
10.22067/ijnao.2026.100999.1981
Abstract
Anthrax is a zoonotic disease that endangers humans and animals and is frequently fatal when left untreated. Its spores persist in the environment, so people in regular contact with livestock, especially frontline workers, remain exposed. Vaccines exist for humans and animals, yet transmission continues, partly because control programmes vaccinate animals while overlooking humans. This study formulates a deterministic model of anthrax transmission that accounts for vaccination, treatment, improperly buried carcasses and contaminated animal products. The control reproduction number $R_C$ is derived and used to establish the stability of the disease-free and endemic equilibria, which determines whether the disease dies out or persists under a given set of controls. A global sensitivity analysis identifies the parameters with the strongest influence on transmission. The model is then extended to an optimal control problem with five time-dependent interventions: environmental decontamination and sterilisation, screening and treatment of infected animals, human vaccination, animal vaccination, and behavioural measures that reduce exposure. Cost-effectiveness analysis shows that human vaccination is the most cost-effective single intervention. Where resources are scarce, human vaccination alone gives the greatest benefit. As resources increase, the preferred options are, in order, human vaccination combined with animal vaccination, then these two together with behavioural measures, and finally a four-control strategy that adds screening and treatment of infected animals. Human vaccination should therefore form the basis of anthrax control programmes. The results offer public health authorities, policymakers and outbreak response teams a ranked set of options for managing future anthrax outbreaks.
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