Mathematical models for vaccination, waning immunity and immune system boosting: a general framework

When the body gets infected by a pathogen or receives a vaccine dose, the immune system develops pathogen-specific immunity. Induced immunity decays in time and years after recovery/vaccination the host might become susceptible again. Exposure to the pathogen in the environment boosts the immune system thus prolonging the duration of the protection. Such an interplay of within host and population level dynamics poses significant challenges in rigorous mathematical modeling of immuno-epidemiology. The aim of this paper is twofold. First, we provide an overview of existing models for waning of disease/vaccine-induced immunity and immune system boosting. Then a new modeling approach is proposed for SIRVS dynamics, monitoring the immune status of individuals and including both waning immunity and immune system boosting. We show that some previous models can be considered as special cases or approximations of our framework.Comment: 18 pages, 1 figure keywords: Immuno-epidemiology, Waning immunity, Immune status, Boosting, Physiological structure, Reinfection, Delay equations, Vaccination. arXiv admin note: substantial text overlap with arXiv:1411.319

Some asymptotic properties of SEIRS models withnonlinear incidence and random delays

This paper presents the dynamics of mosquitoes and humans with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless version is derived; analytical techniques are applied to find conditions for deterministic extinction and permanence of disease. The BRN R0* and ESPR E(e–(μvT1+μT2)) are computed. Conditions for deterministic extinction and permanence are expressed in terms of R0* and E(e–(μvT1+μT2)) and applied to a P. vivax malaria scenario. Numerical results are given

Some asymptotic properties of SEIRS models with nonlinear incidence and random delays

This paper presents the dynamics of mosquitoes and humans with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless version is derived; analytical techniques are applied to find conditions for deterministic extinction and permanence of disease. The BRN  R0* and  ESPR E(e–(μvT1+μT2)) are computed. Conditions for deterministic extinction and permanence are expressed in terms of R0* and E(e–(μvT1+μT2)) and applied to a P. vivax malaria scenario. Numerical results are given

Stability analysis of drinking epidemic models and investigation of optimal treatment strategy

In this research we investigate a class of drinking epidemic models, namely the SPARS type models. The basic reproduction number is derived, and the system dynamical behaviours are investigated for both drinking free equilibrium and drinking persistent equilibrium. The purpose is to determine the long term optimal treatment method and the optimal short period vaccination strategy for controlling the population of the periodic drinkers and alcoholics

The stochastic extinction and stability conditions for a class of malaria epidemic models

The stochastic extinction and stability in the mean of a family of SEIRS malaria models with a general nonlinear incidence rate is presented. The dynamics is driven by independent white noise processes from the disease transmission and natural death rates. The basic reproduction number $R^{*}_{0}$, the expected survival probability of the plasmodium $E(e^{-(\mu_{v}T_{1}+\mu T_{2})})$, and other threshold values are calculated. A sample Lyapunov exponential analysis for the system is utilized to obtain extinction results. Moreover, the rate of extinction of malaria is estimated, and innovative local Martingale and Lyapunov functional techniques are applied to establish the strong persistence, and asymptotic stability in the mean of the malaria-free steady population. %The extinction of malaria depends on $R^{*}_{0}$, and $E(e^{-(\mu_{v}T_{1}+\mu T_{2})})$. Moreover, for either $R^{*}_{0}<1$, or $E(e^{-(\mu_{v}T_{1}+\mu T_{2})})<\frac{1}{R^{*}_{0}}$, whenever $R^{*}_{0}\geq 1$, respectively, extinction of malaria occurs. Furthermore, the robustness of these threshold conditions to the intensity of noise from the disease transmission rate is exhibited. Numerical simulation results are presented.Comment: arXiv admin note: substantial text overlap with arXiv:1808.09842, arXiv:1809.03866, arXiv:1809.0389

The Dynamics Analysis of Two Delayed Epidemic Spreading Models with Latent Period on Heterogeneous Network

Two novel delayed epidemic spreading models with latent period on scale-free network are presented. The formula of the basic reproductive number and the analysis of dynamical behaviors for the models are presented. Meanwhile, numerical simulations are given to verify the main results

Mathematical Modeling, Simulation, and Time Series Analysis of Seasonal Epidemics.

Seasonal and non-seasonal Susceptible-Exposed-Infective-Recovered-Susceptible (SEIRS) models are formulated and analyzed. It is proved that the disease-free steady state of the non-seasonal model is locally asymptotically stable if Rv \u3c 1, and disease invades if Rv \u3e 1. For the seasonal SEIRS model, it is shown that the disease-free periodic solution is locally asymptotically stable when R̅v \u3c 1, and I(t) is persistent with sustained oscillations when R̅v \u3e 1. Numerical simulations indicate that the orbit representing I(t) decays when R̅v \u3c 1 \u3c Rv. The seasonal SEIRS model with routine and pulse vaccination is simulated, and results depict an unsustained decrease in the maximum of prevalence of infectives upon the introduction of routine vaccination and a sustained decrease as pulse vaccination is introduced in the population. Mortality data of pneumonia and influenza is collected and analyzed. A decomposition of the data is analyzed, trend and seasonality effects ascertained, and a forecasting strategy proposed