Indirect interaction between an endemic and an invading pathogen: A case study of Plasmodium and Usutu virus dynamics in a shared bird host population.

Infectious disease agents can influence each other's dynamics in shared host populations. We consider such influence for two mosquito-borne infections where one pathogen is endemic at the time that a second pathogen invades. We regard a setting where the vector has a bias towards biting host individuals infected with the endemic pathogen and where there is a cost to co-infected hosts. As a motivating case study, we regard Plasmodium spp., that cause avian malaria, as the endemic pathogen, and Usutu virus (USUV) as the invading pathogen. Hosts with malaria attract more mosquitoes compared to susceptible hosts, a phenomenon named vector bias. The possible trade-off between the vector-bias effect and the co-infection mortality is studied using a compartmental epidemic model. We focus first on the basic reproduction number R0 for Usutu virus invading into a malaria-endemic population, and then explore the long-term dynamics of both pathogens once Usutu virus has become established. We find that the vector bias facilitates the introduction of malaria into a susceptible population, as well as the introduction of Usutu in a malaria-endemic population. In the long term, however, both a vector bias and co-infection mortality lead to a decrease in the number of individuals infected with either pathogen, suggesting that avian malaria is unlikely to be a promoter of Usutu invasion. This proposed approach is general and allows for new insights into other negative associations between endemic and invading vector-borne pathogens.

Extended-spectrum ß-lactamase- and AmpC ß-lactamase-producing Enterobacterales associated with urinary tract infections in the New Zealand community: a case-control study.

OBJECTIVES: To assess whether having a pet in the home is a risk factor for community-acquired urinary tract infections associated with extended-spectrum ß-lactamase (ESBL)- or AmpC ß-lactamase (ACBL)- producing Enterobacterales. METHODS: An unmatched case-control study was conducted between August 2015 and September 2017. Cases (n = 141) were people with community-acquired urinary tract infection (UTI) caused by ESBL- or ACBL-producing Enterobacterales. Controls (n = 525) were recruited from the community. A telephone questionnaire on pet ownership and other factors was administered, and associations were assessed using logistic regression. RESULTS: Pet ownership was not associated with ESBL- or ACBL-producing Enterobacterales-related human UTIs. A positive association was observed for recent antimicrobial treatment, travel to Asia in the previous year, and a doctor's visit in the last 6 months. Among isolates with an ESBL-/ACBL-producing phenotype, 126/134 (94%) were Escherichia coli, with sequence type 131 being the most common (47/126). CONCLUSIONS: Companion animals in the home were not found to be associated with ESBL- or ACBL-producing Enterobacterales-related community-acquired UTIs in New Zealand. Risk factors included overseas travel, recent antibiotic use, and doctor visits.

Challenges in modelling the dynamics of infectious diseases at the wildlife-human interface.

The Covid-19 pandemic is of zoonotic origin, and many other emerging infections of humans have their origin in an animal host population. We review the challenges involved in modelling the dynamics of wildlife-human interfaces governing infectious disease emergence and spread. We argue that we need a better understanding of the dynamic nature of such interfaces, the underpinning diversity of pathogens and host-pathogen association networks, and the scales and frequencies at which environmental conditions enable spillover and host shifting from animals to humans to occur. The major drivers of the emergence of zoonoses are anthropogenic, including the global change in climate and land use. These, and other ecological processes pose challenges that must be overcome to counterbalance pandemic risk. The development of more detailed and nuanced models will provide better tools for analysing and understanding infectious disease emergence and spread.

Is our breathing optimal? Solving a piecewise linear model with constraints.

This paper is motivated by a question related to the control of amplitude and frequency of breathing. We present a simplified mathematical model, consisting of two piecewise linear ordinary differential equations, that could represent gas exchange in the lungs. We then define and solve an optimal control problem with unknown durations of inhalation and exhalation, subject to several constraints. The durations are divided such that one of the state variables is strictly increasing during the first phase and decreasing during the second phase. The optimal control problem can be solved analytically. One analytical solution is found when the forcing is a given sinusoidal function with unknown period and amplitude. Other analytical solutions are found when the forcing function, the period and the duration of the first phase are unknown but the amplitude is given. Our results show that different cost functions can produce different optimal forcing functions. We also show that the shape of these functions does not affect the average levels of oxygen in the lungs-the average level of oxygen is only dependent on the amplitude and period of breathing in the model we present.

Carriage of Extended-Spectrum-Beta-Lactamase- and AmpC Beta-Lactamase-Producing Escherichia coli Strains from Humans and Pets in the Same Households.

Extended-spectrum-beta-lactamase (ESBL)- or AmpC beta-lactamase (ACBL)-producing Escherichia coli bacteria are the most common cause of community-acquired multidrug-resistant urinary tract infections (UTIs) in New Zealand. The carriage of antimicrobial-resistant bacteria has been found in both people and pets from the same household; thus, the home environment may be a place where antimicrobial-resistant bacteria are shared between humans and pets. In this study, we sought to determine whether members (pets and people) of the households of human index cases with a UTI caused by an ESBL- or ACBL-producing E. coli strain also carried an ESBL- or ACBL-producing Enterobacteriaceae strain and, if so, whether it was a clonal match to the index case clinical strain. Index cases with a community-acquired UTI were recruited based on antimicrobial susceptibility testing of urine isolates. Fecal samples were collected from 18 non-index case people and 36 pets across 27 households. Eleven of the 27 households screened had non-index case household members (8/18 people and 5/36 animals) positive for ESBL- and/or ACBL-producing E. coli strains. Whole-genome sequence analysis of 125 E. coli isolates (including the clinical urine isolates) from these 11 households showed that within seven households, the same strain of ESBL-/ACBL-producing E. coli was cultured from both the index case and another person (5/11 households) or pet dog (2/11 households). These results suggest that transmission within the household may contribute to the community spread of ESBL- or ACBL-producing E. coliIMPORTANCEEnterobacteriaceae that produce extended-spectrum beta-lactamases (ESBLs) and AmpC beta-lactamases (ACBLs) are important pathogens and can cause community-acquired illnesses, such as urinary tract infections (UTIs). Fecal carriage of these resistant bacteria by companion animals may pose a risk for transmission to humans. Our work evaluated the sharing of ESBL- and ACBL-producing E. coli isolates between humans and companion animals. We found that in some households, dogs carried the same strain of ESBL-producing E. coli as the household member with a UTI. This suggests that transmission events between humans and animals (or vice versa) are likely occurring within the home environment and, therefore, the community as a whole. This is significant from a health perspective, when considering measures to minimize community transmission, and highlights that in order to manage community spread, we need to consider interventions at the household level.

Generalised probability mass function for the final epidemic size of an SIR model on a line of triangles network.

We explore the feasibility of deriving generalised expressions for the probability mass function (PMF) of the final epidemic size of a Susceptible - Infected - Recovered (SIR) model on a finite network of an arbitrary number of nodes. Expressions for the probability that the infection progresses along a given pathway in a line of triangles (LoT) network are presented. Deriving expressions for the probability that the infection ends at any given node allows us to determine the corresponding final size of the epidemic, and hence produce PMFs of the final epidemic size. We illustrate how we can use the results from small networks derived in a previous study to describe how an infection spreads through a LoT network. The key here is to correctly decompose the larger network into an appropriate assemblage of small networks.

Eight challenges in modelling disease ecology in multi-host, multi-agent systems.

Many disease systems exhibit complexities not captured by current theoretical and empirical work. In particular, systems with multiple host species and multiple infectious agents (i.e., multi-host, multi-agent systems) require novel methods to extend the wealth of knowledge acquired studying primarily single-host, single-agent systems. We outline eight challenges in multi-host, multi-agent systems that could substantively increase our knowledge of the drivers and broader ecosystem effects of infectious disease dynamics.

Nine challenges for deterministic epidemic models.

Deterministic models have a long history of being applied to the study of infectious disease epidemiology. We highlight and discuss nine challenges in this area. The first two concern the endemic equilibrium and its stability. We indicate the need for models that describe multi-strain infections, infections with time-varying infectivity, and those where superinfection is possible. We then consider the need for advances in spatial epidemic models, and draw attention to the lack of models that explore the relationship between communicable and non-communicable diseases. The final two challenges concern the uses and limitations of deterministic models as approximations to stochastic systems.

Modeling infectious disease dynamics in the complex landscape of global health.

Despite some notable successes in the control of infectious diseases, transmissible pathogens still pose an enormous threat to human and animal health. The ecological and evolutionary dynamics of infections play out on a wide range of interconnected temporal, organizational, and spatial scales, which span hours to months, cells to ecosystems, and local to global spread. Moreover, some pathogens are directly transmitted between individuals of a single species, whereas others circulate among multiple hosts, need arthropod vectors, or can survive in environmental reservoirs. Many factors, including increasing antimicrobial resistance, increased human connectivity and changeable human behavior, elevate prevention and control from matters of national policy to international challenge. In the face of this complexity, mathematical models offer valuable tools for synthesizing information to understand epidemiological patterns, and for developing quantitative evidence for decision-making in global health.

Modelling heterogeneous host immune response in a multi-strain system.

We explore the dynamics that occur when multiple variants of a virus are released in a population, where hosts can make an immune response to only one epitope of the virus. A heterogeneous immune response was implemented by varying the probability for making a response at a locus of the virus variants. A framework based on an SIR model is presented which allows for the explicit representation of the virus variants and the immune histories of the population. From this we are able to calculate the proportion of the population infected by each variant and the number of times a host has been infected when there have been multiple epidemics. When there are discrete epidemics, we use the framework to calculate the proportion of the population infected analytically, demonstrating a method which reduces the calculations required in comparison with solving the full system of differential equations. However, when there are multiple strains present in the population at any time, we show that the full set of ODEs must be solved to fully describe the infection dynamics.

Modelling the epidemiology of hepatitis B in New Zealand.

Hepatitis B is a vaccine preventable disease caused by the hepatitis B virus (HBV) that can induce potentially fatal liver damage. It has the second highest mortality rate of all vaccine preventable diseases in New Zealand. Vaccination against HBV was introduced in New Zealand in 1988, and the country is now categorised with overall low endemicity but with areas of both high and medium endemic levels. We present an SECIR compartmental mathematical model, with the population divided into age classes, for the transmission of HBV using local data on incidence of infection and vaccination coverage. We estimate the basic reproduction number, R(0), to be 1.53, and show that the vaccination campaign has substantially reduced this below one. However, a large number of carriers remain in the population acting as a source of infection.

Modelling the evolution and spread of HIV immune escape mutants.

During infection with human immunodeficiency virus (HIV), immune pressure from cytotoxic T-lymphocytes (CTLs) selects for viral mutants that confer escape from CTL recognition. These escape variants can be transmitted between individuals where, depending upon their cost to viral fitness and the CTL responses made by the recipient, they may revert. The rates of within-host evolution and their concordant impact upon the rate of spread of escape mutants at the population level are uncertain. Here we present a mathematical model of within-host evolution of escape mutants, transmission of these variants between hosts and subsequent reversion in new hosts. The model is an extension of the well-known SI model of disease transmission and includes three further parameters that describe host immunogenetic heterogeneity and rates of within host viral evolution. We use the model to explain why some escape mutants appear to have stable prevalence whilst others are spreading through the population. Further, we use it to compare diverse datasets on CTL escape, highlighting where different sources agree or disagree on within-host evolutionary rates. The several dozen CTL epitopes we survey from HIV-1 gag, RT and nef reveal a relatively sedate rate of evolution with average rates of escape measured in years and reversion in decades. For many epitopes in HIV, occasional rapid within-host evolution is not reflected in fast evolution at the population level.

Early epidemiological assessment of the virulence of emerging infectious diseases: a case study of an influenza pandemic.

BACKGROUND: The case fatality ratio (CFR), the ratio of deaths from an infectious disease to the number of cases, provides an assessment of virulence. Calculation of the ratio of the cumulative number of deaths to cases during the course of an epidemic tends to result in a biased CFR. The present study develops a simple method to obtain an unbiased estimate of confirmed CFR (cCFR), using only the confirmed cases as the denominator, at an early stage of epidemic, even when there have been only a few deaths. METHODOLOGY/PRINCIPAL FINDINGS: Our method adjusts the biased cCFR by a factor of underestimation which is informed by the time from symptom onset to death. We first examine the approach by analyzing an outbreak of severe acute respiratory syndrome in Hong Kong (2003) with known unbiased cCFR estimate, and then investigate published epidemiological datasets of novel swine-origin influenza A (H1N1) virus infection in the USA and Canada (2009). Because observation of a few deaths alone does not permit estimating the distribution of the time from onset to death, the uncertainty is addressed by means of sensitivity analysis. The maximum likelihood estimate of the unbiased cCFR for influenza may lie in the range of 0.16-4.48% within the assumed parameter space for a factor of underestimation. The estimates for influenza suggest that the virulence is comparable to the early estimate in Mexico. Even when there have been no deaths, our model permits estimating a conservative upper bound of the cCFR. CONCLUSIONS: Although one has to keep in mind that the cCFR for an entire population is vulnerable to its variations among sub-populations and underdiagnosis, our method is useful for assessing virulence at the early stage of an epidemic and for informing policy makers and the public.

Hepatitis B in a high prevalence New Zealand population: a mathematical model applied to infection control policy.

BACKGROUND: Chronic hepatitis B (CHB) is a vaccine preventable disease of global public health importance. The prevalence of CHB in New Zealand's Tongan population is over 10%, a level consistent with endemic infection, which contrasts to the low overall New Zealand prevalence (<0.5%). Despite the introduction of infant vaccination in 1988, coverage among Tongan children is estimated to be only 53%. AIMS: To estimate the population benefit of additional public health control measures besides 'business as usual' infant vaccination for hepatitis B in high prevalence populations. METHODS: A mathematical model of hepatitis B virus (HBV) transmission was used to predict future CHB prevalence in the New Zealand Tongan population under different infection control strategies. RESULTS: Prevalence of CHB is predicted to plateau at 2% in the New Zealand Tongan population if coverage remains at current levels, which are therefore insufficient to achieve long-term elimination of HBV. The critical proportion of immunisation coverage for elimination of the virus is estimated to be 73%. The effect of screening for HBV carriage and early disease management was unable to be quantified, but is likely to reduce the population burden of HBV infection and thus contribute to accelerating elimination. CONCLUSIONS AND RECOMMENDATIONS: Mathematical models are a useful tool to forecast the future burden of CHB under a range of control strategy scenarios in high prevalence populations. Serosurveillance and targeted vaccination has similarly arrested HBV transmission in time-series prevalence studies from Taiwan and Alaska. Such a policy may demonstrate similar efficacy in New Zealand ethnic groups with endemic HBV infection.

Key transmission parameters of an institutional outbreak during the 1918 influenza pandemic estimated by mathematical modelling.

AIM: To estimate the key transmission parameters associated with an outbreak of pandemic influenza in an institutional setting (New Zealand 1918). METHODS: Historical morbidity and mortality data were obtained from the report of the medical officer for a large military camp. A susceptible-exposed-infectious-recovered epidemiological model was solved numerically to find a range of best-fit estimates for key epidemic parameters and an incidence curve. Mortality data were subsequently modelled by performing a convolution of incidence distribution with a best-fit incidence-mortality lag distribution. RESULTS: Basic reproduction number (R0) values for three possible scenarios ranged between 1.3, and 3.1, and corresponding average latent period and infectious period estimates ranged between 0.7 and 1.3 days, and 0.2 and 0.3 days respectively. The mean and median best-estimate incidence-mortality lag periods were 6.9 and 6.6 days respectively. This delay is consistent with secondary bacterial pneumonia being a relatively important cause of death in this predominantly young male population. CONCLUSION: These R0 estimates are broadly consistent with others made for the 1918 influenza pandemic and are not particularly large relative to some other infectious diseases. This finding suggests that if a novel influenza strain of similar virulence emerged then it could potentially be controlled through the prompt use of major public health measures.