Abstract
This paper investigates a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies. Firstly, the model is investigated under vaccination of newborns, which is fact in a direct action on the recruitment level of the model. Secondly, it is investigated under a periodic impulsive vaccination on the susceptible in the sense that the vaccination impulses are concentrated in practice in very short time intervals around a set of impulsive time instants subject to constant inter-vaccination periods. Both strategies can be adapted, if desired, to the time-varying levels of susceptible in the sense that the control efforts be increased as those susceptible levels increase. The model is discussed in terms of suitable properties like the positivity of the solutions, the existence and allocation of equilibrium points, and stability concerns related to the values of the basic reproduction number. It is proven that the basic reproduction number lies below unity, so that the disease-free equilibrium point is asymptotically stable for larger values of the disease transmission rates under vaccination controls compared to the case of absence of vaccination. It is also proven that the endemic equilibrium point is not reachable if the disease-free one is stable and that the disease-free equilibrium point is unstable if the reproduction number exceeds unity while the endemic equilibrium point is stable. Several numerical results are investigated for both vaccination rules with the option of adapting through ime the corresponding efforts to the levels of susceptibility. Such simulation examples are performed under parameterizations related to the current SARS-COVID 19 pandemic.
Highlights
Epidemiology—from the Greek epi, demos, and logos—tries to study the distribution and determinant factors of diseases and applies this study to their control and prevention.It integrates procedures and techniques from disciplines such as the biomedical sciences and the social sciences [1,2,3,4]
An SEIR epidemic model is proposed where the host population is split into four categories, namely:
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Summary
Epidemiology—from the Greek epi (about), demos (people), and logos (study)—tries to study the distribution and determinant factors of diseases and applies this study to their control and prevention. If the disease-free equilibrium point is unstable, in the case of a reproduction number exceeding unity, it is shown that it cannot be surrounded by a limit cycle in any of the phase planes; the only stable and attainable attractor being the endemic equilibrium point Another alternative vaccination strategy, which is discussed in the paper under the same basic model, consists of a periodic impulsive vaccination. The mathematical analysis of the model properties is discussed in detail in terms of local and global asymptotic stability concerns of both the disease-free and endemic equilibrium points, which are explicitly calculated as dependent of the vaccination of newborns levels. The vaccine administration strategies can be adapted to the levels of susceptible individuals which can facilitate the administration calendar
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