Asymptotic behavior of an epidemic model with infinitely many variants
We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction number $\mathcal{R}_0$ of the pathogen can be defined in that case and corresponds to a threshold between the persistence ($\mathcal{R}_0>1$) and the extinction ($\mathcal{R}_0\leq 1$) of the pathogen. When $\mathcal{R}_0>1$ and the maximal fitness is attained by at least one variant, we show that the systems reaches an equilibrium state that can be explicitly determined from the initial data. When $\mathcal{R}_0>1$ but none of the variants attain the maximal fitness, the situation is more intricate. We show that, in general, the pathogen is uniformly persistent and any family of variants that have a fitness which is uniformly lower than the optimal fitness, eventually gets extinct. We derive a condition under which the total pathogen population converges to a limit which can be computed explicitly. We also find counterexamples that show that, when our condition is not met, the total pathogen population may converge to an unexpected value, or the system can even reach an eternally transient behavior where the total pathogen population between several values. We illustrate our results with numerical simulations that emphasize the wide variety of possible dynamics.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Accurate closed-form solution of the SIR epidemic model
An accurate closed-form solution is obtained to the SIR Epidemic Model through the use of Asymptotic Approximants (Barlow et. al, 2017, Q. Jl Mech. Appl. Math, 70 (1), 21-48). The solution is created by analytically cont…
FormMathEpicasting: An Ensemble Wavelet Neural Network (EWNet) for Forecasting Epidemics
Infectious diseases remain among the top contributors to human illness and death worldwide, among which many diseases produce epidemic waves of infection. The unavailability of specific drugs and ready-to-use vaccines to…
SchedulingTime SeriesTime Series AnalysisA Novel Stochastic Epidemic Model with Application to COVID-19
In this paper we propose a novel SEIR stochastic epidemic model. A distinguishing feature of this new model is that it allows us to consider a set up under general latency and infectious period distributions. To some ext…
Superinfection and the hypnozoite reservoir for Plasmodium vivax: a multitype branching process approximation
Plasmodium vivax malaria is a mosquito-borne disease of significant public health importance. A defining feature of the within-host biology of P. vivax is the accrual of a hypnozoite reservoir, comprising a bank of quies…
AttributeStochastic Modeling of an Infectious Disease Part II: Simulation Experiments and Verification of the Analysis
In Part 1, we introduced a stochastic model of an infectious disease, based on the BDI (birth and death with immigration) process. We showed that random processes defined by this model can capture the essence of the stoc…