Characterizing the next-generation matrix and basic reproduction number in ecological epidemiology

Dual-strain dynamics of COVID-19 variants in India: Modeling, analysis, and implications for pandemic control

This study introduces a detailed compartmental model developed to understand the complex dynamics of COVID-19 transmission, focusing on the Delta and Omicron variants in India. The model tracks disease progression through different population compartments, considering factors like vaccination, time-dependent transmission, economic burden and COVID-19 death rates, loss of vaccine-induced immunity, and the transition of asymptomatic cases to recovery. The model is validated against established epidemiological knowledge and real-world data, emphasizing dynamic parameterization and accurate representation of immunity dynamics. The basic reproduction number for both variants is calculated, and sensitivity analysis for various parameters is conducted. Time-dependent parameters are estimated using the discrete inverse method. The study also explores the economic burden, impact of different types of masks, vaccine efficacy, and vaccine-induced immunity through numerical analysis. Subject Classification; Primary 92B05, Secondary 62P10.

Impact of vector richness on the risk of vector-borne disease: The role of vector competence

A central goal of disease ecology is to identify the factors that drive the spread of infectious diseases. Changes in vector richness can have complex effects on disease risk, but little is known about the role of vector competence in the relationship between vector richness and disease risk. In this study, we firstly investigated the combined effects of vector competence, interspecific competition, and feeding interference on disease risk through a two-vector, one-host SIR-SI model, and obtained threshold conditions for the occurrence of dilution and amplification effects. Secondly, we extended the above model to the case of N vectors and assumed that all vectors were homogeneous to obtain analytic expressions for disease risk. It was found that in the two-vector model, disease risk declined more rapidly as interspecific competition of the high-competence vector increased. When vector richness increases, the positive effects of adding a high-competence vector species on disease transmission may outweigh the negative effects of feeding interference due to increased vector richness, making an amplification effect more likely to occur. While the addition of a highly competitive vector species may exacerbate the negative effects of feeding interference, making a dilution effect more likely to occur. In the N-vector model, the effect of increased vector richness on disease risk was fully driven by the strength of feeding interference and interspecific competition, and changes in vector competence only quantitatively but not qualitatively altered the vector richness-disease risk relationship. This work clarifies the role of vector competence in the relationship between vector richness and disease risk and provides a new perspective for studying the diversity-disease relationship. It also provides theoretical guidance for vector management and disease prevention strategies.

Quantifying the invasion risk of West Nile virus: Insights from a multi-vector and multi-host SEIR model

The invasion of vector-borne diseases depends on the type of specific features of the vector and hosts at play. Within the Culex pipiens complex, differences in ecology, biology, and vector competence can influence the risk of West Nile virus (WNV) outbreaks. To determine which life-history traits affect WNV invasion into susceptible communities the most, we constructed an epidemiological Susceptible-Exposed-Infectious-Recovered model with three vector (eco)types, Culex pipiens pipiens, Cx. pip. molestus, and their hybrids, and two vertebrate hosts, birds (as amplifying hosts) and humans (as dead-end hosts). We investigated how differences in feeding preferences and transmission rates influenced WNV transmission across different habitats and two seasons (Spring versus Summer), to investigate the impact of increasing mosquitoes on the WNV transmission risk. Our results showed that vector feeding preferences and the transmission rate between mosquitoes and birds were the parameters that most influenced WNV invasion risk. Even though our model did not predict WNV invasion across any of the studied environments, we found that natural habitats displayed the highest susceptibility to WNV invasion. Pipiens (eco)type acted as the primary vector in all habitats. Hybrids, contrary to common opinion, showed minimal involvement in WNV transmission. However, it is important to interpret our study results with caution due to the possibility of idealized spring and summer seasons being reflected in the field-collected data. Our study could be a tool to enhance current vector surveillance and control programs by targeting specific vector types in specific environments, especially in natural habitat, which are most responsive to environmental shifts. The joint approach based on epidemiological modelling based on field collected data can help to reduce wasted time and economic costs while maximizing the efficiency of local public health authorities.

Exploring the influence of competition on arbovirus invasion risk in communities

Arbovirus outbreaks in communities are affected by how vectors, hosts and non-competent species interact. In this study, we investigate how ecological interactions between species and epidemiological processes influence the invasion potential of a vector-borne disease. We use an eco-epidemiological model to explore the basic reproduction number R0 for a range of interaction strengths in key processes, using West Nile virus infection to parameterize the model. We focus our analysis on intra and interspecific competition between vectors and between hosts, as well as competition with non-competent species. We show that such ecological competition has non-linear effects on R0 and can greatly impact invasion risk. The presence of multiple competing vector species results in lower values for R0 while host competition leads to the highest values of risk of disease invasion. These effects can be understood in terms of how the competitive pressures influence the vector-to-host ratio, which has a positive relationship with R0. We also show numerical examples of how vector feeding preferences become more relevant in high competition conditions between hosts. Under certain conditions, non-competent hosts, which can lead to a dilution effect for the pathogen, can have an amplification effect if they compete strongly with the competent hosts, hence facilitating pathogen invasion in the community.

Host community composition, community assembly pattern, and disease transmission mode jointly determine the direction and strength of the diversity-disease relationship

Rapid global biodiversity loss and increasing emerging infectious diseases underscore the significance of identifying the diversity-disease relationship. Although experimental evidence supports the existence of dilution effects in several natural ecosystems, we still know very little about the conditions under which a dilution effect will occur. Using a multi-host Susceptible-Infected-Recovered model, we found when disease transmission was density-dependent, the diversity-disease relationship could exhibit an increasing, decreasing, or non-monotonic trend, which mainly depended on the patterns of community assembly. However, the combined effects of the host competence-abundance relationship and species extinction order may reverse or weaken this trend. In contrast, when disease transmission was frequency-dependent, the diversity-disease relationship only showed a decreasing trend, the host competence-abundance relationship and species extinction order did not alter this decreasing trend, but it could reduce the detectability of the dilution effect and affect disease prevalence. Overall, a combination of disease transmission mode, community assembly pattern, and host community composition determines the direction or strength of the diversity-disease relationship. Our work helps explain why previous studies came to different conclusions about the diversity-disease relationship and provides a deeper understanding of the pathogen transmission dynamics in actual communities.

Host competence, interspecific competition and vector preference interact to determine the vector-borne infection ecology

Understanding how ecological interactions affect vector-borne disease dynamics is crucial in the context of rapid biodiversity loss and increased emerging vector-borne diseases. Although there have been many studies on the impact of interspecific competition and host competence on disease dynamics, few of them have addressed the case of a vector-borne disease. Using a simple compartment model with two competing host species and one vector, we investigated the combined effects of vector preference, host competence, and interspecific competition on disease risk in a vector-borne system. Our research demonstrated that disease transmission dynamics in multi-host communities are more complex than anticipated. Vector preference and differences in host competence shifted the direction of the effect of competition on community disease risk, yet interspecific competition quantitatively but not qualitatively changed the effect of vector preference on disease risk. Our work also identified the conditions of the dilution effect and amplification effect in frequency-dependent transmission mode, and we discovered that adding vector preference and interspecific competition into a simple two-host-one-vector model altered the outcomes of how increasing species richness affects disease risk. Our work explains some of the variation in outcomes in previous empirical and theoretical studies on the dilution effect.

A Novel Epidemic Model for the Interference Spread in the Internet of Things

Due to the multi-technology advancements, internet of things (IoT) applications are in high demand to create smarter environments. Smart objects communicate by exchanging many messages, and this creates interference on receivers. Collection tree algorithms are applied to only reduce the nodes/paths’ interference but cannot fully handle the interference across the underlying IoT. This paper models and analyzes the interference spread in the IoT setting, where the collection tree routing algorithm is adopted. Node interference is treated as a real-life contamination of a disease, where individuals can migrate across compartments such as susceptible, attacked and replaced. The assumed typical collection tree routing model is the least interference beaconing algorithm (LIBA), and the dynamics of the interference spread is studied. The underlying network’s nodes are partitioned into groups of nodes which can affect each other and based on the partition property, the susceptible–attacked–replaced (SAR) model is proposed. To analyze the model, the system stability is studied, and the compartmental based trends are experimented in static, stochastic and predictive systems. The results shows that the dynamics of the system are dependent groups and all have points of convergence for static, stochastic and predictive systems.

Model Predictive Control of COVID-19 Pandemic with Social Isolation and Vaccination Policies in Thailand

This study concerns the COVID-19 pandemic in Thailand related to social isolation and vaccination policies. The behavior of disease spread is described by an epidemic model via a system of ordinary differential equations. The invariant region and equilibrium point of the model, as well as the basic reproduction number, are also examined. Moreover, the model is fitted to real data for the second wave and the third wave of the pandemic in Thailand by a sum square error method in order to forecast the future spread of infectious diseases at each time. Furthermore, the model predictive control technique with quadratic programming is used to investigate the schedule of preventive measures over a time horizon. As a result, firstly, the plan results are proposed to solve the limitation of ICU capacity and increase the survival rate of patients. Secondly, the plan to control the outbreak without vaccination shows a strict policy that is difficult to do practically. Finally, the vaccination plan significantly prevents disease transmission, since the populations who get the vaccination have immunity against the virus. Moreover, the outbreak is controlled in 28 weeks. The results of a measurement strategy for preventing the disease are examined and compared with a control and without a control. Thus, the schedule over a time horizon can be suitably used for controlling.

Infection dynamics in ecosystems: on the interaction between red and grey squirrels, pox virus, pine martens and trees

Ecological and epidemiological processes and interactions influence each other, positively and negatively, directly and indirectly. The invasion potential of pathogens is influenced by the ecosystem context of their host species' populations. This extends to the capacity of (multiple) host species to maintain their (common) pathogen and the way pathogen dynamics are influenced by changes in ecosystem composition. This paper exemplifies these interactions and consequences in a study of red and grey squirrel dynamics in the UK. Differences and changes in background habitat and trophic levels above and below the squirrel species lead to different dynamic behaviour in many subtle ways. The range of outcomes of the different interactions shows that one has to be careful when drawing conclusions about the mechanisms and processes involved in explaining observed phenomena concerning pathogens in their natural environment. The dynamic behaviour also shows that planning interventions, for example for conservation purposes, benefits from understanding the complexity of interactions beyond the particular pathogen and its threatened host species.

Characterizing reservoirs of infection and the maintenance of pathogens in ecosystems

We use a previously published compartmental model of the dynamics of pathogens in ecosystems to define and explore the concepts of maintenance host, maintenance community and reservoir of infection in a full ecological context of interacting host and non-host species. We show that, contrary to their current use in the literature, these concepts can only be characterized relative to the ecosystem in which the host species are embedded, and are not 'life-history traits' of (groups of) species. We give a number of examples to demonstrate that the same (group of) host species can lose or gain maintenance or reservoir capability as a result of a changing ecosystem context, even when these changes primarily affect non-hosts. One therefore has to be careful in designating host species as either maintenance or reservoir in absolute terms.

Quantifying the dilution effect for models in ecological epidemiology

The dilution effect, where an increase in biodiversity results in a reduction in the prevalence of an infectious disease, has been the subject of speculation and controversy. Conversely, an amplification effect occurs when increased biodiversity is related to an increase in prevalence. We explore the conditions under which these effects arise, using multi species compartmental models that integrate ecological and epidemiological interactions. We introduce three potential metrics for quantifying dilution and amplification, one based on infection prevalence in a focal host species, one based on the size of the infected subpopulation of that species and one based on the basic reproduction number. We introduce our approach in the simplest epidemiological setting with two species, and show that the existence and strength of a dilution effect is influenced strongly by the choices made to describe the system and the metric used to gauge the effect. We show that our method can be generalized to any number of species and to more complicated ecological and epidemiological dynamics. Our method allows a rigorous analysis of ecological systems where dilution effects have been postulated, and contributes to future progress in understanding the phenomenon of dilution in the context of infectious disease dynamics and infection risk.

The epidemiological models of Karl-Peter Hadeler

The most frequently cited articles out of KP Hadeler's 45 papers with epidemiological applications are summarized. Parasitic diseases which increase the death rate of the hosts proportional to the integer number of parasites present were described by integral equations for the generating function of the age- and time-dependent number of parasites. A model was derived for a population structured by the continuous level of parasitic infection.

Stimulated by the spread of AIDS a new class of epidemic models was developed which take into account explicitly the formation and separation of pairs. For predator-prey populations with parasitic infections threshold conditions for the persistence of the predator were derived. The interaction of epidemics and demography was analysed. Several epidemiological conditions led to backward bifurcations associated with multiple infective stationary states.

Biodiversity and the Ecology of Emerging Infectious Diseases

The question of how biodiversity influences the emergence of infectious diseases is the subject of ongoing research. A set of nonlinear differential equations is been used to explore the interactions between ecology and epidemiology. The model allows for frequency-dependent transmission of infection within host species, and density-dependent transmission between species, via the environment or a vector. Three examples are discussed. It is shown that removing a pathogen may increase a consumer population, decreasing its resource. It is then shown that the presence of a pathogen could enable a predator and a prey species to coexist. Finally the dilution effect, by which increasing biodiversity reduces the transmission of an infectious disease, is investigated.

Exploring vector-borne infection ecology in multi-host communities: A case study of West Nile virus

In this study, we develop a model to investigate how ecological factors might affect the dynamics of a vector-borne pathogen in a population composed by different hosts which interact with each other. Specifically, we consider the case when different host species compete with each other, as they share the same habitat, and the vector might have different feeding preference, which can also be time dependent. As a prototypical example, we apply our model to study the invasion and spread, during a typical season, of West Nile virus in an ecosystem composed of two competent avian host species and possibly of dead-end host species. We found that competition and vector feeding preferences can profoundly influence pathogen invasion, influencing its probability to start an epidemic, and influencing transmission rates. Finally, when considering time-dependent feeding preferences, as observed in the field, we noted that the virus circulation could be amplified and that the timing of epidemic peaks could be changed. Our work highlights that ecological interactions between hosts can have a profound influence on the dynamics of the pathogen and that, when modeling vector-borne infections, vector feeding behavior should, for this reason, be carefully evaluated.

A comparison of the performance of regression models of Amblyomma americanum (L.) (Ixodidae) using life cycle or landscape data from administrative divisions

The distribution of Amblyomma americanum (L.) in the continental United States has been modelled using the reported distribution in counties as "established" (six or more ticks or two or more life stages were recorded during a specified time period), "reported" (fewer than six ticks of a single life stage were recorded), or "absent" (neither of the above categories were met) and a set of environmental and biotic explanatory variables. Categorical (vegetation, climate, and habitat suitability for the main host of the tick) or continuous variables (raw data on temperature, vegetation, and habitat fragmentation), as well as the processes of the tick's life cycle, were tested to build models using multiple logistic regression. The best results were obtained when the life cycle processes were used as descriptors of regressions. Better models derived from life cycle processes were obtained after inclusion of habitat suitability for the white tailed deer (the main host of the tick) and landscape fragmentation. Using this approach, 86% of "absent" and 83% of "established" counties were classified correctly, but all "reported" counties were erroneously classified. Modelling life cycle processes with descriptions of host abundance and habitat fragmentation produced the best outcome when coordinates were missing. When only standard categorical descriptors of climate or vegetation were included in models, results produced poor outcomes. Models were improved with remotely sensed information on temperature and vegetation but produced high rates of misclassification for 14% of "absent", 37% of "established", and 100% of "reported" counties. Modelling produced poor results in the absence of point distributions (coordinates). Therefore, "reported" counties cannot be handled adequately by modelling procedures, probably because this category does not reflect the true status of the tick distribution. We conclude that standard categorical classifications of the distribution of an organism can not be reliably used as input for modelling procedures.

How mathematical epidemiology became a field of biology: a commentary on Anderson and May (1981) 'The population dynamics of microparasites and their invertebrate hosts'

We discuss the context, content and importance of the paper ‘The population dynamics of microparasites and their invertebrate hosts’, by R. M. Anderson and R. M. May, published in the Philosophical Transactions of the Royal Society as a stand-alone issue in 1981. We do this from the broader perspective of the study of infectious disease dynamics, rather than the specific perspective of the dynamics of insect pathogens. We argue that their 1981 paper fits seamlessly in the systematic study of infectious disease dynamics that was initiated by the authors in 1978, combining effective use of simple mathematical models, firmly rooted in biology, with observable or empirically measurable ingredients and quantities, and promoting extensive capacity building. This systematic approach, taking ecology and biology rather than applied mathematics as the motivation for advance, proved essential for the maturation of the field, and culminated in their landmark textbook of 1991. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Selective breeding: the future of TB management in African buffalo?

The high prevalence of bovine tuberculosis (BTB) in African buffalo (Syncerus caffer) in regions of southern African has a negative economic impact on the trade of animals and animal products, represents an ecological threat to biodiversity, and poses a health risk to local communities through the wildlife-cattle-human interface. Test and cull methods may not be logistically feasible in many free-range wildlife systems, and with the presence of co-existing BTB hosts and the limited effectiveness of the BCG vaccine in buffalo, there is a need for alternative methods of BTB management. Selective breeding for increased resistance to BTB in buffalo may be a viable method of BTB management in the future, particularly if genetic information can be incorporated into these schemes. To explore this possibility, we discuss the different strategies that can be employed in selective breeding programmes, and consider the implementation of genetic improvement schemes. We reflect on the suitability of applying this strategy for enhanced BTB resistance in African buffalo, and address the challenges of this approach that must be taken into account. Conclusions and the implications for management are presented.

Infectious disease agents mediate interaction in food webs and ecosystems

Infectious agents are part of food webs and ecosystems via the relationship with their host species that, in turn, interact with both hosts and non-hosts. Through these interactions, infectious agents influence food webs in terms of structure, functioning and stability. The present literature shows a broad range of impacts of infectious agents on food webs, and by cataloguing that range, we worked towards defining the various mechanisms and their specific effects. To explore the impact, a direct approach is to study changes in food-web properties with infectious agents as separate species in the web, acting as additional nodes, with links to their host species. An indirect approach concentrates not on adding new nodes and links, but on the ways that infectious agents affect the existing links across host and non-host nodes, by influencing the 'quality' of consumer-resource interaction as it depends on the epidemiological state host involved. Both approaches are natural from an ecological point of view, but the indirect approach may connect more straightforwardly to commonly used tools in infectious disease dynamics.

Evolution of pathogen virulence under selective predation: a construction method to find eco-evolutionary cycles

We investigate eco-evolutionary cycles in the joint dynamics of pathogen virulence and predator population density when hosts carrying virulent infections are exposed to increased risk of predation. We introduce a new technique to find trade-off functions under which the model exhibits limit cycles; this technique provides a constructive proof that the system is able to generate limit cycles, and can be applied to other eco-evolutionary models as well. We also study a concrete example to confirm that eco-evolutionary cycles occur in a significant part of the parameter space and to briefly explore other evolutionary outcomes in the same model.