Samit Bhattacharyya

Statistical physics of vaccination

Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination - one of the most important preventive measures of modern times - is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research.

A game dynamic model for delayer strategies in vaccinating behaviour for pediatric infectious diseases.

Several studies have found that some parents delay the age at which their children receive pediatric vaccines due to perception of higher vaccine risk at the recommended age of vaccination. This has been particularly apparently during the Measles-Mumps-Rubella scare in the United Kingdom. Under a voluntary vaccination policy, vaccine coverage in certain age groups is a potentially complex interplay between vaccinating behaviour, disease dynamics, and age-specific risk factors. Here, we construct an age-structured game dynamic model, where individuals decide whether to vaccinate according to imitation dynamics depending on age-dependent disease prevalence and perceived risk of vaccination. Individuals may be timely vaccinators, delayers, or non-vaccinators. The model exhibits multiple equilibria and a broad range of possible dynamics. For certain parameter regimes, the proportion of timely vaccinators and delayers oscillate in an anti-phase fashion in response to oscillations in infection prevalence. Under an exogenous change to the perceived risk of vaccination as might occur during a vaccine scare, the model can also capture an increase in delayer strategists similar in magnitude to that observed during the Measles-Mumps-Rubella vaccine scare in the United Kingdom. Our model also shows that number of delayers steadily increases with increasing severity of the scare, whereas it saturates to specific value with increases in duration of the scare. Finally, by comparing the model dynamics with and without the option of a delayer strategy, we show that adding a third delayer strategy can have a stabilizing effect on model dynamics. In an era where individual choice--rather than accessibility--is becoming an increasingly important determinant of vaccine uptake, more infectious disease models may need to use game theory or related techniques to determine vaccine uptake.

Rapid emergence of free-riding behavior in new pediatric immunization programs.

Background Mathematical models have formalized how free-rider effects can threaten the stability of high vaccine coverage levels under established voluntary vaccination programs. However, little research has addressed the question of when free-riding begins to develop when a new vaccine is first introduced in a population. Methodology/Principal Findings Here, we combine a game theoretical model of vaccinating behavior with an age-structured compartmental model to analyze rational vaccinating behavior in the first years of a universal immunization program, where a new vaccine is free to all children of a specified age. The model captures how successive birth cohorts face different epidemiological landscapes that have been shaped by the vaccinating decisions of previous birth cohorts, resulting in a strategic interaction between individuals in different birth cohorts. The model predicts a Nash equilibrium coverage level of for the first few birth cohorts under the new program. However, free-riding behavior emerges very quickly, with the Nash equilibrium vaccine coverage dropping significantly within 2-5 years after program initiation. Subsequently, a rich set of coupled dynamics between infection prevalence and vaccinating behaviors is possible, ranging from relatively stable (but reduced) coverage in later birth cohorts to wide fluctuations in vaccine coverage from one birth cohort to the next. Individual tolerance for vaccine risk also starts out at relatively high levels before dropping significantly within a few years. Conclusions/Significance These results suggest that even relatively new immunization programs can be vulnerable to drops in vaccine coverage caused by vaccine scares and exacerbated by herd immunity effects, necessitating vigilance from the start.

Cross-immunity between strains explains the dynamical pattern of paramyxoviruses

Significance Pathogens that invoke an immune response immediately after infection can also provide partial cross-protection against other strains of the same or closely related pathogens. This cross-protection can shape the epidemiological dynamics of multistrain pathogens when an epidemic of one strain temporarily suppresses the transmission of another. Identifying these interactions from time series of epidemiological data is difficult, particularly when prevalence oscillates seasonally. We use long-term incidence data on Respiratory Syncytial Virus (RSV), three serotypes of Human Parainfluenza Virus (HPIV), and Human Metapneumovirus to study mathematical models of different mechanisms of pathogen interaction. Our results show a strong signal of cross-protection from RSV in controlling the timing and magnitude of HPIV outbreaks, and a stronger interaction with more closely related serotypes. Viral respiratory tract diseases pose serious public health problems. Our ability to predict and thus, be able to prepare for outbreaks is strained by the complex factors driving the prevalence and severity of these diseases. The abundance of diseases and transmission dynamics of strains are not only affected by external factors, such as weather, but also driven by interactions among viruses mediated by human behavior and immunity. To untangle the complex out-of-phase annual and biennial pattern of three common paramyxoviruses, Respiratory Syncytial Virus (RSV), Human Parainfluenza Virus (HPIV), and Human Metapneumovirus (hMPV), we adopt a theoretical approach that integrates ecological and immunological mechanisms of disease interactions. By estimating parameters from multiyear time series of laboratory-confirmed cases from the intermountain west region of the United States and using statistical inference, we show that models of immune-mediated interactions better explain the data than those based on ecological competition by convalescence. The strength of cross-protective immunity among viruses is correlated with their genetic distance in the phylogenetic tree of the paramyxovirus family.

Role of word-of-mouth for programs of voluntary vaccination: A game-theoretic approach.

We propose a model describing the synergetic feedback between word-of-mouth (WoM) and epidemic dynamics controlled by voluntary vaccination. The key feature consists in combining a game-theoretic model for the spread of WoM and a compartmental model describing VSIR disease dynamics in the presence of a program of voluntary vaccination. We evaluate and compare two scenarios for determinants of behavior, depending on what WoM disseminates: (1) vaccine advertising, which may occur whether or not an epidemic is ongoing and (2) epidemic status, notably disease prevalence. Understanding the synergy between the two strategies could be particularly important for designing voluntary vaccination campaigns. We find that, in the initial phase of an epidemic, vaccination uptake is determined more by vaccine advertising than the epidemic status. As the epidemic progresses, epidemic status becomes increasingly important for vaccination uptake, considerably accelerating vaccination uptake toward a stable vaccination coverage.

Optimal control of vertically transmitted disease: an integrated approach

We study the dynamics of a disease under administration of a vaccine and antiviral drug, where the disease transmits directly from the parents to the offspring (vertical transmission) and also through contact with infective individuals (horizontal transmission). While vaccination to those susceptible reduces the horizontal transmission, administration of the antiviral drug to infected individuals lessens the chance of vertical transmission. Thus the vaccine and antiviral drug play different roles in controlling the disease, which has both vertical and horizontal transmission. We develop a 3D model with Susceptible-Infected-Recovered under vaccination to the susceptible and antiviral treatment to the infected and consider a control theoretic approach using the Pontryagin maximum principle to analyse the cost-effectiveness of the control process. Our results demonstrate that a mixed intervention strategy of vaccination and antiviral drug in a proper ratio is the most effective way to control the disease. We show that cost-effectiveness of both intervention strategies intimately depends on disease-related parameters, such as force of infection, probability of being infected to offspring from infected mothers, loss of immunity or reinfection and also on cost of treatment.

Age-specific mixing generates transient outbreak risk following critical-level vaccination.

Measles elimination goals have been adopted in a range of countries, sub-regions, and regions since the WHO declared an elimination goal by 2015 or 2020. All countries attempt to achieve and maintain high coverage through routine immunization programmes. This routine strategy, however, does not ensure the elimination goal of measles. Many developed countries, such as the United States, that have succeeded in interrupting measles transmission earlier, are now experiencing outbreaks with an increasing number of cases. Using a stochastic, age-structured model of measles vaccination dynamics, we explore and characterize the transient dynamics of measles susceptibility in the years following the implementation of routine vaccination at the herd immunity threshold. We demonstrate how a population could face risks of potentially large outbreaks even within few years of vaccination. We characterize different risk profiles depending on the incidence pattern in the years prior to vaccination. These results suggest that the classic critical vaccination threshold is necessary to achieve herd immunity, but not sufficient to prevent long periods of transient, super-critical dynamics. Our results suggest the need of future work for more careful monitoring of the impacts of current immunization programmes, and developing models that take into account more complicated vaccination strategies, demographic factors, and population movements.

Clinical characteristics of onchocerciasis-associated epilepsy in villages in Maridi County, Republic of South Sudan

PURPOSE To describe the clinical manifestations of persons with epilepsy (PWE) in onchocerciasis endemic villages in South Sudan. METHODS During a survey in Maridi County in May 2018, PWE were interviewed and examined in their households by a clinical officer or medical doctor. Onchocerciasis-associated epilepsy (OAE) was defined as ≥2 seizures without any obvious cause, starting between the ages of 3-18 years in previously healthy persons who had resided for at least 3 years in the onchocerciasis endemic area. RESULTS Seven hundred and thirty-six PWE were included in the study; 315 (42.8%) were females; median age was 18 years. A variety of seizure types were reported: generalized tonic-clonic seizures in 511 PWE (69.4%), absences in 15 (2.0%), focal motor seizures with full awareness in 7 (1.0%), focal motor seizures with impaired awareness in 25 (3.4%), brief episodes of hallucinations in 316 (43.9%) and nodding seizures in 335 (45.5%). The median age of onset of all seizures was 10 years, and 8 years for nodding seizures. PWE with nodding seizures presented with more cognitive disabilities. The diagnostic criteria for OAE were met by 414 (85.2%) of the 486 PWE with complete information. Eighty (11.0%) PWE presented with Nakalanga features. Only 378 (51.4%) PWE were taking anti-epileptic treatment. CONCLUSION PWE presented with a wide spectrum of seizures. The high percentage of PWE who met the diagnostic criteria for OAE suggests that better onchocerciasis control could prevent new cases. Urgent action is needed to close the anti-epileptic treatment gap.

Species interactions may help explain the erratic periodicity of whooping cough dynamics

Incidence of whooping cough exhibits variable dynamics across time and space. The periodicity of this disease varies from annual to five years in different geographic regions in both developing and developed countries. Many hypotheses have been put forward to explain this variability such as nonlinearity and seasonality, stochasticity, variable recruitment of susceptible individuals via birth, immunization, and immune boosting. We propose an alternative hypothesis to describe the variability in periodicity - the intricate dynamical variability of whooping cough may arise from interactions between its dominant etiological agents of Bordetella pertussis and Bordetella parapertussis. We develop a two-species age-structured model, where two pathogens are allowed to interact by age-dependent convalescence of individuals with severe illness from infections. With moderate strength of interactions, the model exhibits multi-annual coexisting attractors that depend on the R0 of the two pathogens. We also examine how perturbation from case importation and noise in transmission may push the system from one dynamical regime to another. The coexistence of multi-annual cycles and the behavior of switching between attractors suggest that variable dynamics of whopping cough could be an emergent property of its multi-agent etiology.

Oscillation in Pest Population and Its Management: A Mathematical Study

We study the role of predation dynamics in oscillation of pest population in insect ecology. A two-dimensional pest control model (under the use of insecticides) with time delay in predation is considered in this paper. By the Hopf bifurcation theory, we prove the existence of the stable oscillation of the system. We also consider the economic viability of the control process. First we improve the Pontryagin maximum principle (PMP) where the delay in the system is sufficiently small and control function is linear, and then we apply the improved version of PMP to perform the optimal analysis of the pest control model as a special case.