Mosquito ageing modulates the development, virulence and transmission potential of pathogens.

Host age variation is a striking source of heterogeneity that can shape the evolution and transmission dynamic of pathogens. Compared with vertebrate systems, our understanding of the impact of host age on invertebrate-pathogen interactions remains limited. We examined the influence of mosquito age on key life-history traits driving human malaria transmission. Females of Anopheles coluzzii, a major malaria vector, belonging to three age classes (4-, 8- and 12-day-old), were experimentally infected with Plasmodium falciparum field isolates. Our findings revealed reduced competence in 12-day-old mosquitoes, characterized by lower oocyst/sporozoite rates and intensities compared with younger mosquitoes. Despite shorter median longevities in older age classes, infected 12-day-old mosquitoes exhibited improved survival, suggesting that the infection might act as a fountain of youth for older mosquitoes specifically. The timing of sporozoite appearance in the salivary glands remained consistent across mosquito age classes, with an extrinsic incubation period of approximately 13 days. Integrating these results into an epidemiological model revealed a lower vectorial capacity for older mosquitoes compared with younger ones, albeit still substantial owing to extended longevity in the presence of infection. Considering age heterogeneity provides valuable insights for ecological and epidemiological studies, informing targeted control strategies to mitigate pathogen transmission.

Growth bound and threshold dynamic for nonautonomous nondensely defined evolution problems.

We propose a general framework for simultaneously calculating the threshold value for population growth and determining the sign of the growth bound of the evolution family generated by the problem below [Formula: see text]where [Formula: see text] is a Hille-Yosida linear operator (possibly unbounded, non-densely defined) on a Banach space [Formula: see text], and the maps [Formula: see text], [Formula: see text] are p-periodic in time and continuous in the operator norm topology. We give applications of our approach for two general examples of an age-structured model, and a delay differential system. Other examples concern the dynamics of a nonlocal problem arising in population genetics and the dynamics of a structured human-vector malaria model.

Linking within- and between-host scales for understanding the evolutionary dynamics of quantitative antimicrobial resistance.

Understanding both the epidemiological and evolutionary dynamics of antimicrobial resistance is a major public health concern. In this paper, we propose a nested model, explicitly linking the within- and between-host scales, in which the level of resistance of the bacterial population is viewed as a continuous quantitative trait. The within-host dynamics is based on integro-differential equations structured by the resistance level, while the between-host scale is additionally structured by the time since infection. This model simultaneously captures the dynamics of the bacteria population, the evolutionary transient dynamics which lead to the emergence of resistance, and the epidemic dynamics of the host population. Moreover, we precisely analyze the model proposed by particularly performing the uniform persistence and global asymptotic results. Finally, we discuss the impact of the treatment rate of the host population in controlling both the epidemic outbreak and the average level of resistance, either if the within-host scale therapy is a success or failure. We also explore how transitions between infected populations (treated and untreated) can impact the average level of resistance, particularly in a scenario where the treatment is successful at the within-host scale.

Understanding dynamics of Plasmodium falciparum gametocytes production: Insights from an age-structured model.

Many models of within-host malaria infection dynamics have been formulated since the pioneering work of Anderson et al. in 1989. Biologically, the goal of these models is to understand what governs the severity of infections, the patterns of infectiousness, and the variation thereof across individual hosts. Mathematically, these models are based on dynamical systems, with standard approaches ranging from K-compartments ordinary differential equations (ODEs) to delay differential equations (DDEs), to capture the relatively constant duration of replication and bursting once a parasite infects a host red blood cell. Using malariatherapy data, which offers fine-scale resolution on the dynamics of infection across a number of individual hosts, we compare the fit and robustness of one of these standard approaches (K-compartments ODE) with a partial differential equations (PDEs) model, which explicitly tracks the "age" of an infected cell. While both models perform quite similarly in terms of goodness-of-fit for suitably chosen K, the K-compartments ODE model particularly overestimates parasite densities early on in infections when the number of repeated compartments is not large enough. Finally, the K-compartments ODE model (for suitably chosen K) and the PDE model highlight a strong qualitative connection between the density of transmissible parasite stages (i.e., gametocytes) and the density of host-damaging (and asexually-replicating) parasite stages. This finding provides a simple tool for predicting which hosts are most infectious to mosquitoes -vectors of Plasmodium parasites- which is a crucial component of global efforts to control and eliminate malaria.

Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic.

In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing.

Within-host bacterial growth dynamics with both mutation and horizontal gene transfer.

The evolution and emergence of antibiotic resistance is a major public health concern. The understanding of the within-host microbial dynamics combining mutational processes, horizontal gene transfer and resource consumption, is one of the keys to solving this problem. We analyze a generic model to rigorously describe interactions dynamics of four bacterial strains: one fully sensitive to the drug, one with mutational resistance only, one with plasmidic resistance only, and one with both resistances. By defining thresholds numbers (i.e. each strain's effective reproduction and each strain's transition threshold numbers), we first express conditions for the existence of non-trivial stationary states. We find that these thresholds mainly depend on bacteria quantitative traits such as nutrient consumption ability, growth conversion factor, death rate, mutation (forward or reverse), and segregational loss of plasmid probabilities (for plasmid-bearing strains). Next, concerning the order in the set of strain's effective reproduction thresholds numbers, we show that the qualitative dynamics of the model range from the extinction of all strains, coexistence of sensitive and mutational resistance strains, to the coexistence of all strains at equilibrium. Finally, we go through some applications of our general analysis depending on whether bacteria strains interact without or with drug action (either cytostatic or cytotoxic).

[Mathematical epidemiology and modeling of the Covid-19 pandemic: issues and diversity]. / Épidémiologie mathématique et modélisation de la pandémie de Covid-19 : enjeux et diversité.

During the COVID-19 pandemic, the field of mathematical epidemiology experienced an exceptional production and media coverage of its work. Even though data and knowledge on the emerging disease were patchy, a wide variety of models were developed and applied in unprecedented timeframes, with the aim of estimating the reproduction number, the starting date of the epidemic or the cumulative incidence, but also to explore different scenarios of non-pharmaceutical interventions. Their results have made a major contribution to epidemiological surveillance and informed public health policy decisions.

Mosaics often outperform pyramids: insights from a model comparing strategies for the deployment of plant resistance genes against viruses in agricultural landscapes.

The breakdown of plant virus resistance genes is a major issue in agriculture. We investigated whether a set of resistance genes would last longer when stacked into a single plant cultivar (pyramiding) or when deployed individually in regional mosaics (mosaic strategy). We modeled the genetic and epidemiological processes shaping the demogenetic dynamics of viruses under a multilocus gene-for-gene system, from the plant to landscape scales. The landscape consisted of many fields, was subject to seasonality, and of a reservoir hosting viruses year-round. Strategy performance depended principally on the fitness costs of adaptive mutations, epidemic intensity before resistance deployment and landscape connectivity. Mosaics were at least as good as pyramiding strategies in most production situations tested. Pyramiding strategies performed better only with slowly changing virus reservoir dynamics. Mosaics are more versatile than pyramiding strategies, and we found that deploying a mosaic of three to five resistance genes generally provided effective disease control, unless the epidemics were driven mostly by within-field infections. We considered the epidemiological and evolutionary mechanisms underlying the greater versatility of mosaics in our case study, with a view to providing breeders and growers with guidance as to the most appropriate deployment strategy.

Optimal control for an age-structured model for the transmission of hepatitis B.

One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formulated an age-structured model for the transmission dynamics of HBV with differential infectivity: symptomatic and asymptomatic infections. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which minimizes HBV-related deaths as well as the costs associated with intervention.

Mathematical model of Ehrlichia chaffeensis transmission dynamics in dogs.

Ehrlichia chaffeensis is a tick-borne disease transmitted by ticks to dogs. Few studies have mathematical modelled such tick-borne disease in dogs, and none have developed models that incorporate different ticks' developmental stages (discrete variable) as well as the duration of infection (continuous variable). In this study, we develop and analyze a model that considers these two structural variables using integrated semigroups theory. We address the well-posedness of the model and investigate the existence of steady states. The model exhibits a disease-free equilibrium and an endemic equilibrium. We calculate the reproduction number (T0). We establish a necessary and sufficient condition for the bifurcation of an endemic equilibrium. Specifically, we demonstrate that a bifurcation, either backward or forward, can occur at T0=1, leading to the existence, or not, of an endemic equilibrium even when T0<1. Finally, numerical simulations are employed to illustrate these theoretical findings.

An epi-evolutionary model for predicting the adaptation of spore-producing pathogens to quantitative resistance in heterogeneous environments.

We have modeled the evolutionary epidemiology of spore-producing plant pathogens in heterogeneous environments sown with several cultivars carrying quantitative resistances. The model explicitly tracks the infection-age structure and genetic composition of the pathogen population. Each strain is characterized by pathogenicity traits determining its infection efficiency and a time-varying sporulation curve taking into account lesion aging. We first derived a general expression of the basic reproduction number R 0 for fungal pathogens in heterogeneous environments. We show that the evolutionary attractors of the model coincide with local maxima of R 0 only if the infection efficiency is the same on all host types. We then studied the contribution of three basic resistance characteristics (the pathogenicity trait targeted, resistance effectiveness, and adaptation cost), in interaction with the deployment strategy (proportion of fields sown with a resistant cultivar), to (i) pathogen diversification at equilibrium and (ii) the shaping of transient dynamics from evolutionary and epidemiological perspectives. We show that quantitative resistance affecting only the sporulation curve will always lead to a monomorphic population, whereas dimorphism (i.e., pathogen diversification) can occur if resistance alters infection efficiency, notably with high adaptation costs and proportions of the resistant cultivar. Accordingly, the choice of the quantitative resistance genes operated by plant breeders is a driver of pathogen diversification. From an evolutionary perspective, the time to emergence of the evolutionary attractor best adapted to the resistant cultivar tends to be shorter when resistance affects infection efficiency than when it affects sporulation. Conversely, from an epidemiological perspective, epidemiological control is always greater when the resistance affects infection efficiency. This highlights the difficulty of defining deployment strategies for quantitative resistance simultaneously maximizing epidemiological and evolutionary outcomes.

Memory is key in capturing COVID-19 epidemiological dynamics.

SARS-CoV-2 virus has spread over the world rapidly creating one of the largest pandemics ever. The absence of immunity, presymptomatic transmission, and the relatively high level of virulence of the COVID-19 infection led to a massive flow of patients in intensive care units (ICU). This unprecedented situation calls for rapid and accurate mathematical models to best inform public health policies. We develop an original parsimonious discrete-time model that accounts for the effect of the age of infection on the natural history of the disease. Analysing the ongoing COVID-19 in France as a test case, through the publicly available time series of nationwide hospital mortality and ICU activity, we estimate the value of the key epidemiological parameters and the impact of lock-down implementation delay. This work shows that including memory-effects in the modelling of COVID-19 spreading greatly improves the accuracy of the fit to the epidemiological data. We estimate that the epidemic wave in France started on Jan 20 [Jan 12, Jan 28] (95% likelihood interval) with a reproduction number initially equal to 2.99 [2.59, 3.39], which was reduced by the national lock-down started on Mar 17 to 24 [21, 27] of its value. We also estimate that the implementation of the latter a week earlier or later would have lead to a difference of about respectively -13k and +50k hospital deaths by the end of lock-down. The present parsimonious discrete-time framework constitutes a useful tool for now- and forecasting simultaneously community incidence and ICU capacity strain.

Optimizing the early detection of low pathogenic avian influenza H7N9 virus in live bird markets.

In Southeast Asia, surveillance at live bird markets (LBMs) has been identified as crucial for detecting avian influenza viruses (AIV) and reducing the risk of human infections. However, the design of effective surveillance systems in LBMs remains complex given the rapid turn-over of poultry. We developed a deterministic transmission model to provide guidance for optimizing AIV surveillance efforts. The model was calibrated to fit one of the largest LBMs in northern Vietnam at high risk of low pathogenic H7N9 virus introduction from China to identify the surveillance strategy that optimizes H7N9 detection. Results show that (i) using a portable diagnostic device would slightly reduce the number of infected birds leaving the LBM before the first detection, as compared to a laboratory-based diagnostic strategy, (ii) H7N9 detection could become more timely by sampling birds staying overnight, just before new susceptible birds are introduced at the beginning of a working day, and (iii) banning birds staying overnight would represent an effective intervention to reduce the risk of H7N9 spread but would decrease the likelihood of virus detection if introduced. These strategies should receive high priority in Vietnam and other Asian countries at risk of H7N9 introduction.

A Dynamical and Zero-Inflated Negative Binomial Regression Modelling of Malaria Incidence in Limpopo Province, South Africa.

Recent studies have considered the connections between malaria incidence and climate variables using mathematical and statistical models. Some of the statistical models focused on time series approach based on Box-Jenkins methodology or on dynamic model. The latter approach allows for covariates different from its original lagged values, while the Box-Jenkins does not. In real situations, malaria incidence counts may turn up with many zero terms in the time series. Fitting time series model based on the Box-Jenkins approach and ARIMA may be spurious. In this study, a zero-inflated negative binomial regression model was formulated for fitting malaria incidence in Mopani and Vhembe-two of the epidemic district municipalities in Limpopo, South Africa. In particular, a zero-inflated negative binomial regression model was formulated for daily malaria counts as a function of some climate variables, with the aim of identifying the model that best predicts reported malaria cases. Results from this study show that daily rainfall amount and the average temperature at various lags have a significant influence on malaria incidence in the study areas. The significance of zero inflation on the malaria count was examined using the Vuong test and the result shows that zero-inflated negative binomial regression model fits the data better. A dynamical climate-based model was further used to investigate the population dynamics of mosquitoes over the two regions. Findings highlight the significant roles of Anopheles arabiensis on malaria transmission over the regions and suggest that vector control activities should be intense to eradicate malaria in Mopani and Vhembe districts. Although An. arabiensis has been identified as the major vector over these regions, our findings further suggest the presence of additional vectors transmitting malaria in the study regions. The findings from this study offer insight into climate-malaria incidence linkages over Limpopo province of South Africa.