Honoring the life and legacy of Fred Brauer.

The work of Fred Brauer (1932-2021) broke new ground in several areas of mathematical population biology, especially mathematical epidemiology and population management. This special issue reflects his legacy: the lines of inquiry he opened, the impact of his research and his books, and his mentoring of generations of young researchers. This dedication highlights milestones in his career and connects his work to the contributions in this issue.

How heterogeneity in density dependence affects disease spread: when lifestyle matters.

People's lifestyles play a major role in disease risk. Some employment sectors and transport modes involve fixed exposures regardless of community size, while in other settings exposure tracks with population density. MERS-CoV, a coronavirus discovered in Saudi Arabia in 2012 closely related to those causing SARS and COVID-19, appears to need extended contact time for transmission, making some segments of a community at greater risk than others. We model mathematically how heterogeneity in contact rate structure impacts disease spread, using as a case study a MERS outbreak in two Saudi Arabian communities. We divide the at-risk population into segments with exposure rates either independent of population density or density-dependent. Analysis shows disease spread is minimized for intermediate size populations with a limited proportion of individuals in the density-independent group. In the case study, the high proportion of density-independent exposure may explain the historical outbreak's extinction in the larger city.

How influenza vaccination and virus interference may impact combined influenza-coronavirus disease burden.

Demand for influenza vaccine rose as countries prepared for the second COVID-19 wave over the winter months of 2020-2021. High coverage of the influenza vaccine can significantly reduce morbidity and mortality of the burden of influenza. Natural influenza infection creates short-term non-specific immunity against respiratory viruses (virus interference). We model two viral diseases, both of the SEIR type, to investigate whether the influenza vaccine increases the combined disease burden of influenza and COVID-19 in a dual outbreak. We show that the combined disease burden's behavior depends on virus interference factors and the proportion of the population vaccinated against influenza. Our results indicate that influenza vaccination only lowers the overall disease burden when net virus interference is relatively low.

Competition between obligate and facultative scavengers and infection: vulture-jackal-anthrax dynamics in Etosha National Park.

Different species of scavengers may compete for the same food in an ecosystem. This case study considers the competition between jackals and vultures in Etosha National Park in Namibia. While jackals are facultative scavengers, able to hunt for food if necessary, vultures are obligate scavengers wholly dependent on carcasses of animals like zebras for persistence. This competition may be further affected by outbreaks of infections such as anthrax, which temporarily increase the number of carcasses but lower the zebra population, acting in some ways as a third competitor. We use a dynamical system to model the interplay between competition dynamics and infection dynamics, and how it is affected by the nature of the competition: indirect (exploitative) or direct (interference). A bifurcation analysis using reproduction numbers shows how vultures' survival may depend on their direct competitive edge in reaching carcasses faster than jackals, and how the infection and the scavengers complicate each other's persistence. Vultures' interference causes a backward bifurcation which enables them to persist. One possible outcome is a "strange bedfellows" bistability in which anthrax and vultures persist only together, not apart, despite being competitors.

Impact of cattle on joint dynamics and disease burden of Japanese encephalitis and leptospirosis.

Japanese encephalitis (JE) is a mosquito-borne neglected tropical disease. JE is mostly found in rural areas where people usually keep cattle at home for their needs. Cattle in households reduce JE virus infections since they distract vectors and act as a dead-end host for the virus. However, the presence of cattle introduces risk of leptospirosis infections in humans. Leptospirosis is a bacterial disease that spreads through direct or indirect contact of urine of the infected cattle. Thus, cattle have both positive and negative impacts on human disease burden. This study uses a mathematical model to study the joint dynamics of these two diseases in the presence of cattle and to identify the net impact of cattle on the annual disease burden in JE-prevalent areas. Analysis indicates that the presence of cattle helps to reduce the overall disease burden in JE-prevalent areas. However, this reduction is dominated by the vector's feeding pattern. To the best of our knowledge, this is the first study to examine the joint dynamics of JE and leptospirosis.

A Mathematical Modeling Study: Assessing Impact of Mismatch Between Influenza Vaccine Strains and Circulating Strains in Hajj.

The influenza virus causes severe respiratory illnesses and deaths worldwide every year. It spreads quickly in an overcrowded area like the annual Hajj pilgrimage in Saudi Arabia. Vaccination is the primary strategy for protection against influenza. Due to the occurrence of antigenic shift and drift of the influenza virus, a mismatch between vaccine strains and circulating strains of influenza may occur. The objective of this study is to assess the impact of mismatch between vaccine strains and circulating strains during Hajj, which brings together individuals from all over the globe. To this end, we develop deterministic mathematical models of influenza with different populations and strains from the northern and southern hemispheres. Our results show that the existence and duration of an influenza outbreak during Hajj depend on vaccine efficacy. In this concern, we discuss four scenarios: vaccine strains for both groups match/mismatch circulating strains, and vaccine strains match their target strains and mismatch the other strains. Further, there is a scenario where a novel pandemic strain arises. Our results show that as long as the influenza vaccines match their target strains, there will be no outbreak of strain H1N1 and only a small outbreak of strain H3N2. Mismatching for non-target strains causes about 10,000 new H3N2 cases, and mismatching for both strains causes about 2,000 more new H1N1 cases and 6,000 additional H3N2 cases during Hajj. Complete mismatch in a pandemic scenario may infect over 342,000 additional pilgrims (13.75%) and cause more cases in their home countries.

Decoys and Dilution: The Impact of Incompetent Hosts on Prevalence of Chagas Disease.

Biodiversity is commonly believed to reduce risk of vector-borne zoonoses. However, researchers already showed that the effect of biodiversity on disease transmission is not that straightforward. This study focuses on the effect of biodiversity, specifically on the effect of the decoy process (additional hosts distracting vectors from their focal host), on reducing infections of vector-borne diseases in humans. Here, we consider the specific case of Chagas disease and use mathematical population models to observe the impact on human infection of the proximity of chickens, which are incompetent hosts for the parasite but serve as a preferred food source for vectors. We consider three cases as the distance between the two host populations varies: short (when farmers bring chickens inside the home to protect them from predators), intermediate (close enough for vectors with one host to detect the presence of the other host type), and far (separate enclosed buildings such as a home and hen-house). Our analysis shows that the presence of chickens reduces parasite prevalence in humans only at an intermediate distance under the condition that the vector birth rate from feeding on chickens is sufficiently low.

Impact of dogs with deltamethrin-impregnated collars on prevalence of visceral leishmaniasis.

Leishmaniasis is a vector borne zoonosis which is classified as a neglected tropical disease. Among the three most common forms of the disease, Visceral Leishmaniasis (VL) is the most threatening to human health, causing 20,000 to 30,000 deaths worldwide each year. Areas where VL is mostly endemic have unprotected dogs in community and houses. The "presence of dogs usually increases VL risk for humans since dogs are the principal reservoir host for the parasite of the disease. Based on this fact, most earlier studies consider culling dogs as a control measure for the spread of VL. A more recent control measure has been the use of deltamethrin-impregnated dog collars ( D I D C s) to protect both humans and dogs by putting D I D C s on dogs neck. The presence of dogs helps to grow the sandfly population faster by offering a more suitable blood-meal source. On the other hand, the presence of D I D C s on dogs helps to reduce sandfly population by the lethality of deltamethrin insecticide. This study brings an ecological perspective to this public health concern, aiming to understand the impact of an additional host (here, protected dogs) on disease risk to a primary host (here, humans). To answer this question, we compare two different settings: a community without dogs, and a community with dogs protected with D I D C . Our analysis shows the presence of protected dogs can reduce VL infection risk in humans. However, this disease risk reduction depends on dogs' tolerance for sandfly bites.

Dynamics of two pathogens in a single tick population.

A mathematical model for a two-pathogen, one-tick, one-host system is presented and explored. The model system is based on the dynamics of Amblyomma americanum, Rickettsia parkeri, and Rickettsia amblyommatis. The goal of this model is to determine how long an invading pathogen, R. parkeri, persists within a tick population, A. americanum, in which a resident pathogen, R. amblyommatis, is already established. The numerical simulations of the model demonstrate the parameter ranges that allow for coexistence of the two pathogens. Sensitivity analysis highlights the importance of vector-borne, tick-to-host, transmission rates on the invasion reproductive number and persistence of the pathogens over time. The model is then applied to a case study based on a reclaimed swampland field site in south-eastern Virginia using field and laboratory data. The results pinpoint the thresholds required for persistence of both pathogens in the local tick population. However, R. parkeri, is not predicted to persist beyond 3 years. Understanding the persistence and coexistence of tick-borne pathogens will allow public health officials increased insight into tick-borne disease dynamics.

Ebola: Impact of hospital's admission policy in an overwhelmed scenario.

Infectious disease outbreaks sometimes overwhelm healthcare facilities. A recent case occurred in West Africa in 2014 when an Ebola virus outbreak overwhelmed facilities in Sierra Leone, Guinea and Liberia. In such scenarios, how many patients can hospitals admit to minimize disease burden? This study considers what type of hospital admission policy during a hypothetical Ebola outbreak can better serve the community, if overcrowding degrades the hospital setting. Our result shows that which policy minimizes loss to the community depends on the initial estimation of the control reproduction number, R0. When the outbreak grows extremely fast (R0 ≫ 1) it is better (in terms of total disease burden) to stop admitting patients after reaching the carrying capacity because overcrowding in the hospital makes the hospital setting ineffective at containing infection, but when the outbreak grows only a little faster than the system's ability to contain it (R0 ≳ 1), it is better to admit patients beyond the carrying capacity because limited overcrowding still reduces infection more in the community. However, when R0 is no more than a little greater than 1 (for our parameter values, 1.012), both policies result the same because the number of patients never exceeds the maximum capacity.

Host switching vs. host sharing in overlapping sylvatic Trypanosoma cruzi transmission cycles.

The principle of competitive exclusion is well established for multiple populations competing for the same resource, and simple models for multistrain infection exhibit it as well when cross-immunity precludes coinfections. However, multiple hosts provide niches for different pathogens to occupy simultaneously. This is the case for the vector-borne parasite Trypanosoma cruzi in overlapping sylvatic transmission cycles in the Americas, where it is enzootic. This study uses cycles in the USA involving two different hosts but the same vector species as a context for the study of the mechanisms behind the communication between the two cycles. Vectors dispersing in search of new hosts may be considered to move between the two cycles (host switching) or, more simply, to divide their time between the two host types (host sharing). Analysis considers host switching as an intermediate case between isolated cycles and intermingled cycles (host sharing) in order to examine the role played by the host-switching rate in permitting coexistence of multiple strains in a single-host population. Results show that although the population dynamics (demographic equilibria) in host-switching models align well with those in the limiting models (host sharing or isolated cycles), infection dynamics differ significantly, in ways that sometimes illuminate the underlying epidemiology (such as differing host susceptibilities to infection) and sometimes reveal model limitations (such as host switching dominating the infection dynamics). Numerical work suggests that the model explains the trace presence of TcI in raccoons but not the more significant co-persistence observed in woodrats.

Agent-based mathematical modeling as a tool for estimating Trypanosoma cruzi vector-host contact rates.

The parasite Trypanosoma cruzi, spread by triatomine vectors, affects over 100 mammalian species throughout the Americas, including humans, in whom it causes Chagas' disease. In the U.S., only a few autochthonous cases have been documented in humans, but prevalence is high in sylvatic hosts (primarily raccoons in the southeast and woodrats in Texas). The sylvatic transmission of T. cruzi is spread by the vector species Triatoma sanguisuga and Triatoma gerstaeckeri biting their preferred hosts and thus creating multiple interacting vector-host cycles. The goal of this study is to quantify the rate of contacts between different host and vector species native to Texas using an agent-based model framework. The contact rates, which represent bites, are required to estimate transmission coefficients, which can be applied to models of infection dynamics. In addition to quantitative estimates, results confirm host irritability (in conjunction with host density) and vector starvation thresholds and dispersal as determining factors for vector density as well as host-vector contact rates.