Journal of Advances in Mathematics and Computer Science

Quarantine occupies an unusual position in the quantitative literature on mpox. It is among the most frequently simulated control measures in transmission models of monkeypox virus (MPXV), yet it is among the least precisely specified. The 2022 multi-country outbreak driven by clade IIb, and the subsequent expansion of clade I transmission in central and eastern Africa, prompted a rapid proliferation of compartmental, network and individual-based models in which a quarantine class or a quarantine rate is used to represent the removal of exposed or infectious individuals from effective contact. This review examines how the quarantine construct has been defined, parameterised, calibrated and interpreted across that literature, and asks whether the resulting policy claims are supported by the evidence on which they rest. Literature was identified through structured searches of accessible scholarly indexes and metadata services, supplemented by backward and forward citation searching and by consultation of authoritative institutional sources, and was appraised against criteria covering construct validity, structural assumptions, parameter provenance, calibration, uncertainty treatment and inferential logic. Six critical findings emerge. Quarantine of exposed contacts and isolation of symptomatic cases are routinely conflated, so that reported effect sizes refer to different interventions under a single label. Deterministic homogeneous-mixing architectures dominate, although MPXV transmission is strongly overdispersed and network-structured. Quarantine parameters are typically assumed rather than estimated, and sensitivity analyses are frequently conducted over invented rather than empirical ranges. The recurrent result that raising the quarantine rate reduces the reproduction number is largely a structural consequence of model formulation rather than an empirical discovery. Data-anchored analyses reach substantially more conditional conclusions than parameter-sweep analyses. Empirical evaluations of isolation and contact tracing report weak certainty of effect and substantial operational failure, particularly in endemic settings. Quarantine effectiveness is contingent on clade, transmission route, detection delay and adherence, and models that omit these contingencies overstate what quarantine can achieve. Priorities include construct standardisation, joint estimation of detection and isolation delays, and explicit representation of adherence and equity constraints.