Modeling rates of infection with transient maternal antibodies and waning active immunity: application to Bordetella pertussis in Sweden

Analysis of the current status of TB transmission in China based on an age heterogeneity model

Tuberculosis (TB) is an infectious disease transmitted through the respiratory system. China is one of the countries with a high burden of TB. Since 2004, an average of more than 800,000 cases of active TB has been reported each year in China. Analyzing the case data from 2004 to 2018, we found significant differences in TB incidence by age group. A model of TB is put forward to explore the effect of age heterogeneity on TB transmission. The nonlinear least squares method is used to obtain the key parameters in the model, and the basic reproduction number Rv = 0.8017 is calculated and the sensitivity analysis of Rv to the parameters is given. The simulation results show that reducing the number of new infections in the elderly population and increasing the recovery rate of elderly patients with the disease could significantly reduce the transmission of TB. Furthermore, the feasibility of achieving the goals of the World Health Organization (WHO) End TB Strategy in China is assessed, and we obtained that with existing TB control measures it will take another 30 years for China to reach the WHO goal to reduce 90% of the number of new cases by the year 2049. However, in theory it is feasible to reach the WHO strategic goal of ending TB by 2035 if the group contact rate in the elderly population can be reduced, though it is difficult to reduce the contact rate.

Modeling the waning and boosting of immunity from infection or vaccination

Immunity following natural infection or immunization may wane, increasing susceptibility to infection with time since infection or vaccination. Symptoms, and concomitantly infectiousness, depend on residual immunity. We quantify these phenomena in a model population composed of individuals whose susceptibility, infectiousness, and symptoms all vary with immune status. We also model age, which affects contact, vaccination and possibly waning rates. The resurgences of pertussis that have been observed wherever effective vaccination programs have reduced typical disease among young children follow from these processes. As one example, we compare simulations with the experience of Sweden following resumption of pertussis vaccination after the hiatus from 1979 to 1996, reproducing the observations leading health authorities to introduce booster doses among school-aged children and adolescents in 2007 and 2014, respectively. Because pertussis comprises a spectrum of symptoms, only the most severe of which are medically attended, accurate models are needed to design optimal vaccination programs where surveillance is less effective.

Inferring infection hazard in wildlife populations by linking data across individual and population scales

Our ability to infer unobservable disease-dynamic processes such as force of infection (infection hazard for susceptible hosts) has transformed our understanding of disease transmission mechanisms and capacity to predict disease dynamics. Conventional methods for inferring FOI estimate a time-averaged value and are based on population-level processes. Because many pathogens exhibit epidemic cycling and FOI is the result of processes acting across the scales of individuals and populations, a flexible framework that extends to epidemic dynamics and links within-host processes to FOI is needed. Specifically, within-host antibody kinetics in wildlife hosts can be short-lived and produce patterns that are repeatable across individuals, suggesting individual-level antibody concentrations could be used to infer time since infection and hence FOI. Using simulations and case studies (influenza A in lesser snow geese and Yersinia pestis in coyotes), we argue that with careful experimental and surveillance design, the population-level FOI signal can be recovered from individual-level antibody kinetics, despite substantial individual-level variation. In addition to improving inference, the cross-scale quantitative antibody approach we describe can reveal insights into drivers of individual-based variation in disease response, and the role of poorly understood processes such as secondary infections, in population-level dynamics of disease.

COMPUTATION OF ℛ IN AGE-STRUCTURED EPIDEMIOLOGICAL MODELS WITH MATERNAL AND TEMPORARY IMMUNITY

For infectious diseases such as pertussis, susceptibility is determined by immunity, which is chronological age-dependent. We consider an age-structured epidemiological model that accounts for both passively acquired maternal antibodies that decay and active immunity that wanes, permitting reinfection. The model is a 6-dimensional system of partial differential equations (PDE). By assuming constant rates within each age-group, the PDE system can be reduced to an ordinary differential equation (ODE) system with aging from one age-group to the next. We derive formulae for the effective reproduction number ℛ and provide their biological interpretation in some special cases. We show that the disease-free equilibrium is stable when ℛ < 1 and unstable if ℛ > 1.