International Journal of Biomathematics · 2018 · 38 citations · 33 references
VaccinationInfectious Disease ModelingControl StrategyMathematical ModelingContact TracingInfectious Disease ModellingGlobal HealthEpidemiological DynamicHigh Contact TracingContact NetworkVirologyMedium IsolationDisease OutbreakBiostatisticsMedium Contact TracingPublic HealthMedicineEpidemiology
More than 20 outbreaks of Ebola virus disease have occurred in Africa since 1976, and yet no adequate treatment is available. Hence, prevention, control measures and supportive treatment remain the only means to avoid the disease. Among these measures, contact tracing occupies a prominent place. In this paper, we propose a simple mathematical model that incorporates imperfect contact tracing, quarantine and hospitalization (or isolation). The control reproduction number [Formula: see text] of each sub-model and for the full model are computed. Theoretically, we prove that when [Formula: see text] is less than one, the corresponding model has a unique globally asymptotically stable disease-free equilibrium. Conversely, when [Formula: see text] is greater than one, the disease-free equilibrium becomes unstable and a unique globally asymptotically stable endemic equilibrium arises. Furthermore, we numerically support the analytical results and assess the efficiency of different control strategies. Our main observation is that, to eradicate EVD, the combination of high contact tracing (up to 90%) and effective isolation is better than all other control measures, namely: (1) perfect contact tracing, (2) effective isolation or full hospitalization, (3) combination of medium contact tracing and medium isolation.
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The Mathematics of Infectious Diseases
Herbert W. Hethcote · SIAM Review · 2000 · 6.7K citations
Replacement Number R, Disease Models, Infectious Disease Modeling +15
Ordinary Differential Equations.
C. E. Langenhop, G. Birkhoff, G.-C Rota · American Mathematical Monthly · 1963 · 1.3K citations
Numerical Analysis, Spectral Theory, Regular Singular Points +8