We present a new analysis of relationships between disease incidence and the prevalence of an experimentally defined state of `recent infection'. This leads to a clean separation between biological parameters (properties of disease progression as reflected in a test for recent infection), which need to be calibrated, and epidemiological state variables, which are estimated in a cross-sectional survey. The framework takes into account the possibility that details of the assay and host/pathogen chemistry leave a (knowable) fraction of the population in the recent category for all times. This systematically addresses an issue which is the source of some controversy about the appropriate use of the BED assay for defining recent HIV infection. Analysis of relative contributions of error arising variously from statistical considerations and simplifications of general expressions indicate that statistical error dominates heavily over all sources of bias for realistic epidemiological and biological scenarios. Numerical calculations validate the approximations made in analytical relations.
Despite high vaccine coverage, pertussis has re-emerged as a public health concern in many countries. One hypothesis posed for re-emergence is the waning of immunity. In some disease systems, the process of waning immunity can be non-linear, involving a complex relationship between the duration of immunity and subsequent boosting of immunity through asymptomatic re-exposure. We present and analyse a model of infectious disease transmission to examine the interplay between infection and immunity. By allowing the duration of infection-acquired immunity to differ from that of vaccine-acquired imm…
Epidemic models are increasingly used in real-world networks to understand diffusion phenomena (such as the spread of diseases, emotions, innovations, failures) or the transport of information (such as news, memes in social on-line networks). A new analysis of the prevalence, the expected number of infected nodes in a network, is presented and physically interpreted. The analysis method is based on spectral decomposition and leads to a universal, analytic curve, that can bound the time-varying prevalence in any finite time interval. Moreover, that universal curve also applies to various types …
We investigate theoretically if treatment alone can reduce the schistosomiasis's prevalence in an infected population, in a long-lasting sustainable way. We use a non-linear system of ordinary differential equations (a SI system combined with a logistic population growth) which describes the time evolution of the non-infected and infected populations, in terms of the recovering, infection, and demographic rates. Our model leads to the conclusion that the only way to eliminate this endemic disease is to implement public health policies aimed at both treatment and environment. We apply our model…
Despite a low global prevalence, infections with Sarcoptes scabiei, or scabies, are still common in remote communities such as in northern Australia and the Solomon Islands. Mass drug administration (MDA) has been utilised in these communities, and although prevalence drops substantially initially, these reductions have not been sustained. We develop a compartmental model of scabies infection dynamics and incorporate both ovicidal and non-ovicidal treatment regimes. By including the dynamics of mass drug administration, we are able to reproduce the phenomena of an initial reduction in prevalen…
There are many sources of data giving information about the number of SARS-CoV-2 infections in the population, but all have major drawbacks, including biases and delayed reporting. For example, the number of confirmed cases largely underestimates the number of infections, deaths lag infections substantially, while test positivity rates tend to greatly overestimate prevalence. Representative random prevalence surveys, the only putatively unbiased source, are sparse in time and space, and the results come with a big delay. Reliable estimates of population prevalence are necessary for understandi…
COVID-19 has forced quarantine measures in several countries across the world. These measures have proven to be effective in significantly reducing the prevalence of the virus. To date, no effective treatment or vaccine is available. In the effort of preserving both public health as well as the economical and social textures, France and Italy governments have partially released lockdown measures. Here we extrapolate the long-term behavior of the epidemics in both countries using a Susceptible-Exposed-Infected-Recovered (SEIR) model where parameters are stochastically perturbed to handle the un…
Empirical studies suggest that contact patterns follow heterogeneous inter-event times, meaning that intervals of high activity are followed by periods of inactivity. Combined with birth and death of individuals, these temporal constraints affect the spread of infections in a non-trivial way and are dependent on the particular contact dynamics. We propose a stochastic model to generate temporal networks where vertices make instantaneous contacts following heterogeneous inter-event times, and leave and enter the system at fixed rates. We study how these temporal properties affect the prevalence…
Mina and Andersen, authors of the Perspectives in Science: COVID-19 Testing: One Size Does Not Fit All have referred to results and adopted conclusions from recently published governmental report Pavelka et al. "The effectiveness of population wide, rapid antigen test based screening in reducing SARS-CoV-2 infection prevalence in Slovakia" without critical consideration, and rigorous verification. We demonstrate that the authors refer to conclusions that are not supported by experimental data. Further, there is a lack of objective, independent information and studies regarding the widespread, …
While the mechanisms and quantitative details are complex, few analysts would doubt that antibiotic use increases the prevalence of drug-resistant bacterial pathogens among all bacteria causing disease in a population. The causal connection between antibiotic use and the total incidence of severe bacterial infections, possibly mediated by antibiotic resistance, is less clearly established. The increasing burden of severe bacterial infections and their sequelae, particularly sepsis, in the United States and other countries, calls out for an explanation. In this Perspective we consider the evide…
The bacterium Group A Streptococcus (Streptococcus pyogenes, GAS) is a human-specific pathogen and a major cause of global morbidity and mortality. Despite decades of research our knowledge of GAS infection and immunity is incomplete, hampering vaccine design and other efforts to reduce disease prevalence. Epidemiological studies indicate positive associations between the prevalence of GAS-related disease, the diversity of circulating strains and the degree of poverty in host populations. However, the infection and immune mechanisms underlying these associations are not clear. In this work, we…
The transmission dynamics of Tuberculosis (TB) involve complex epidemiological and socio-economical interactions between individuals living in highly distinct regional conditions. The level of exogenous reinfection and first time infection rates within high-incidence settings may influence the impact of control programs on TB prevalence. This study aims at enhancing the understanding of TB dynamics via the study of scenarios, within {\it simplified}, two patch, risk-defined environments, in the presence of short term mobility and variations in reinfection and infection rates. The modeling fram…
Mass campaigns with antimalarial drugs are potentially a powerful tool for local elimination of malaria, yet current diagnostic technologies are insufficiently sensitive to identify all individuals who harbor infections. At the same time, overtreatment of uninfected individuals increases the risk of accelerating emergence of drug resistance and losing community acceptance. Local heterogeneity in transmission intensity may allow campaign strategies that respond to index cases to successfully target subpatent infections while simultaneously limiting overtreatment. While selective targeting of ho…
Efficient allocation of limited medical resources is crucial for controlling epidemic spreading on networks. Based on the susceptible-infected-susceptible model, we solve an optimization problem as how best to allocate the limited resources so as to minimize the prevalence, providing that the curing rate of each node is positively correlated to its medical resource. By quenched mean-field theory and heterogeneous mean-field (HMF) theory, we prove that epidemic outbreak will be suppressed to the greatest extent if the curing rate of each node is directly proportional to its degree, under which …
Background: National or local laws, norms or regulations (sometimes and in some countries) require medical providers to report notifiable diseases to public health authorities. Reporting, however, is almost always incomplete. This is due to a variety of reasons, ranging from not recognizing the diseased to failures in the technical or administrative steps leading to the final official register in the disease notification system. The reported fraction varies from 9% to 99% and is strongly associated with the disease being reported. Methods: In this paper we propose a method to approximately est…
Many infectious diseases can lead to re-infection. We examined the relationship between the prevalence of repeat infection and the basic reproductive number (R0). First we solved a generic, deterministic compartmental model of re-infection to derive an analytic solution for the relationship. We then numerically solved a disease specific model of syphilis transmission that explicitly tracked re-infection. We derived a generic expression that reflects a non-linear and monotonically increasing relationship between proportion re-infection and R0 and which is attenuated by entry/exit rates and reco…
Sexually transmitted infections (STIs) continue to present a complex and costly challenge to public health programs. The preferences and social dynamics of a population can have a large impact on the course of an outbreak as well as the effectiveness of interventions intended to influence individual behavior. In addition, individuals may alter their sexual behavior in response to the presence of STIs, creating a feedback loop between transmission and behavior. We investigate the consequences of modeling the interaction between STI transmission and prophylactic use with a model that links a Sus…
Infection by distinct Dengue virus serotypes and host immunity are intricately linked. In particular, certain levels of cross-reactive antibodies in the host may actually enhance infection severity leading to Dengue hemorrhagic fever (DHF). The coupled immunological and epidemiological dynamics of Dengue calls for a multi-scale modeling approach. In this work, we formulate a within-host model which mechanistically recapitulates characteristics of antibody dependent enhancement (ADE) in Dengue infection. The within-host scale is then linked to epidemiological spread by a vector-host partial dif…
Random mixing in host populations has been a convenient simplifying assumption in the study of epidemics, but neglects important differences in contact rates within and between population groups. For HIV/AIDS, the assumption of random mixing is inappropriate for epidemics that are concentrated in groups of people at high risk, including female sex workers (FSW) and their male clients (MCF), injection drug users (IDU) and men who have sex with men (MSM). To find out who transmits infection to whom and how that affects the spread and containment of infection remains a major empirical challenge i…
We analyze a mathematical model of the epizootic of Hantavirus in mice population, including the effect of species which compete with the host. We show that the existence of the second species has an important consequence for the prevalence of the infectious agent in the host. When the two mice species survive in the ecosystem, the competitive pressure of the second species may lead to reduction or complete elimination of the prevalence of infection. The transition between the disappearance of the infection and its presence occurs at a critical value of the competitor's population, resembling …
Co-infecting parasites and pathogens remain a leading challenge for global public health due to their consequences for individual-level infection risk and disease progression. However, a clear understanding of the population-level consequences of co-infection is lacking. Here, we constructed a model that includes three individual-level effects of co-infection: mortality, fecundity, and transmission. We used the model to investigate how these individual-level consequences of co-infection scale up to produce population-level infection patterns. To parameterize this model, we conducted a four-yea…
Renewal equations are a popular approach used in modelling the number of new infections, i.e., incidence, in an outbreak. We develop a stochastic model of an outbreak based on a time-varying variant of the Crump-Mode-Jagers branching process. This model accommodates a time-varying reproduction number and a time-varying distribution for the generation interval. We then derive renewal-like integral equations for incidence, cumulative incidence and prevalence under this model. We show that the equations for incidence and prevalence are consistent with the so-called back-calculation relationship. …
Multipartite viruses replicate through a puzzling evolutionary strategy. Their genome is segmented into two or more parts, and encapsidated in separate particles that appear to propagate independently. Completing the replication cycle, however, requires the full genome, so that a systemic infection of a host requires the concurrent presence of several particles. This represents an apparent evolutionary drawback of multipartitism, while its advantages remain unclear. A transition from monopartite to multipartite viral forms has been described in vitro under conditions of high multiplicity of in…
Chlamydia trachomatis is the most commonly reported infectious disease in the United States and causes important reproductive morbidity in women. The Centers for Disease Control and Prevention have recommended routine screening of sexually active women under age 25 but have not recommended screening among men. Consequently, untested and untreated men may serve as a reservoir of infection in women. Despite three decades of screening women, the chlamydia prevalence has continued to increase. Moreover, chlamydia is five times more common in African American (AA) youth compared to Whites, constitu…
Mathematical models are instrumental to forecast the spread of pathogens and to evaluate the effectiveness of non-pharmaceutical measures. A plethora of optimal strategies has been recently developed to minimize either the infected peak prevalence (IPP) or the epidemic final size (EFS). While most of the control strategies optimize a simple cost function along a fixed finite-time horizon, no consensus has been reached about how to simultaneously handle the IPP, the EFS, and the avoiding of new cycles of infections rebounding. In this work, based on the characterization of the dynamical behavio…
This paper investigates the dynamics of infectious diseases with a non-exponentially distributed infectious period. This is achieved by considering a multi-stage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to t…
We formulate a compartmental model for the propagation of a respiratory disease in a patchy environment. The patches are connected through the mobility of individuals, and we assume that disease transmission and recovery are possible during travel. Moreover, the migration terms are assumed to depend on the distance between patches and the perceived severity of the disease. The positivity and boundedness of the model solutions are discussed. We analytically show the existence and global asymptotic stability of the disease-free equilibrium. We study three different network topologies numerically…
Sexual contacts are the main spreading route of HIV. This puts sex workers at higher risk of infection even in populations where HIV prevalence is moderate or low. Alongside condom use, Pre-Exposure Prophylaxis (PrEP) is an effective tool for sex workers to reduce their risk of HIV acquisition. However, PrEP provides no direct protection against sexually transmitted infections (STIs) other than HIV, unlike condoms. We use an empirical network of sexual contacts among female sex workers (FSWs) and clients to simulate the spread of HIV and gonorrhea. We then investigate the effect of PrEP adopti…
Understanding models which represent the invasion of network-based systems by infectious agents can give important insights into many real-world situations, including the prevention and control of infectious diseases and computer viruses. Here we consider Markovian susceptible-infectious-susceptible (SIS) dynamics on finite strongly connected networks, applicable to several sexually transmitted diseases and computer viruses. In this context, a theoretical definition of endemic prevalence is easily obtained via the quasi-stationary distribution (QSD). By representing the model as a percolation …
Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian es…
We investigate a two-strain disease model with amplification to simulate the prevalence of drug-susceptible (s) and drug-resistant (m) disease strains. We model the emergence of drug resistance as a consequence of inadequate treatment, i.e. amplification. We perform a dynamical analysis of the resulting system and find that the model contains three equilibrium points: a disease-free equilibrium; a mono-existent disease-endemic equilibrium with respect to the drug-resistant strain; and a co-existent disease-endemic equilibrium where both the drug-susceptible and drug-resistant strains persist. …
Hepatitis C virus (HCV) infection is endemic in people who inject drugs (PWID), with prevalence estimates above 60 percent for PWID in the United States. Previous modeling studies suggest that direct acting antiviral (DAA) treatment can lower overall prevalence in this population, but treatment is often delayed until the onset of advanced liver disease (fibrosis stage 3 or later) due to cost. Lower cost interventions featuring syringe access (SA) and medically assisted treatment (MAT) for addiction are known to be less costly, but have shown mixed results in lowering HCV rates below current le…
We develop and analyze an ordinary differential equation model to assess the potential effectiveness of infecting mosquitoes with the Wolbachia bacteria to control the ongoing mosquito-borne epidemics, such as dengue fever, chikungunya, and Zika. Wolbachia is a natural parasitic microbe that stops the proliferation of the harmful viruses inside the mosquito and reduces disease transmission. It is difficult to sustain an infection of the maternal transmitted Wolbachia in a wild mosquito population because of the reduced fitness of the Wolbachia-infected mosquitoes and cytoplasmic incompatibilit…
Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the disease spread. Connecting the scales from individual to population can help inform drug and vaccine development. Thus the value of understanding the impact of immunological parameters on epidemiological quantities. Here we consider an age-since-infe…
Mathematical models of infectious diseases exhibit robust dynamics such as stable endemic or a disease-free equilibrium, or convergence of the solutions to periodic epidemic waves. The present work shows that the accuracy of such dynamics can be significantly improved by incorporating both local and global dynamics of the infection in disease models. To demonstrate improved accuracies, we extended a standard Susceptible-Infected-Recovered (SIR) model by incorporating global dynamics of the COVID-19 pandemic. The extended SIR model assumes three possibilities for the susceptible individuals tra…
Existing compartmental models in epidemiology are limited in terms of optimizing the resource allocation to control an epidemic outbreak under disease growth uncertainty. In this study, we address this core limitation by presenting a multi-stage stochastic programming compartmental model, which integrates the uncertain disease progression and resource allocation to control an infectious disease outbreak. The proposed multi-stage stochastic program involves various disease growth scenarios and optimizes the distribution of treatment centers and resources while minimizing the total expected numb…
The basic reproduction number ($R_0$) is a threshold parameter for disease extinction or survival in isolated populations. However no human population is fully isolated from other human or animal populations. We use compartmental models to derive simple rules for the basic reproduction number for populations with local person-to-person transmission and exposure from some other source: either a reservoir exposure or imported cases. We introduce the idea of a reservoir-driven or importation-driven disease: diseases that would become extinct in the population of interest without reservoir exposur…
Despite the enormous relevance of zoonotic infections to world- wide public health, and despite much effort in modeling individual zoonoses, a fundamental understanding of the disease dynamics and the nature of outbreaks arising in such systems is still lacking. We introduce a simple stochastic model of susceptible-infected- recovered dynamics in a coupled animal-human metapopulation, and solve analytically for several important properties of the cou- pled outbreaks. At early timescales, we solve for the probability and time of spillover, and the disease prevalence in the animal population at …
