Genotypic-phenotypic landscape computation based on first principle and deep learning.

The relationship between genotype and fitness is fundamental to evolution, but quantitatively mapping genotypes to fitness has remained challenging. We propose the Phenotypic-Embedding theorem (P-E theorem) that bridges genotype-phenotype through an encoder-decoder deep learning framework. Inspired by this, we proposed a more general first principle for correlating genotype-phenotype, and the P-E theorem provides a computable basis for the application of first principle. As an application example of the P-E theorem, we developed the Co-attention based Transformer model to bridge Genotype and Fitness model, a Transformer-based pre-train foundation model with downstream supervised fine-tuning that can accurately simulate the neutral evolution of viruses and predict immune escape mutations. Accordingly, following the calculation path of the P-E theorem, we accurately obtained the basic reproduction number (${R}_0$) of SARS-CoV-2 from first principles, quantitatively linked immune escape to viral fitness and plotted the genotype-fitness landscape. The theoretical system we established provides a general and interpretable method to construct genotype-phenotype landscapes, providing a new paradigm for studying theoretical and computational biology.

Characteristics of the Sexual Networks of Men Who Have Sex With Men in Montréal, Toronto, and Vancouver: Insights from Canada's 2022 Mpox Outbreak.

BACKGROUND: The 2022-2023 global mpox outbreak disproportionately affected gay, bisexual, and other men who have sex with men (GBM). We investigated differences in GBM's sexual partner distributions across Canada's 3 largest cities and over time, and how they shaped transmission. METHODS: The Engage Cohort Study (2017-2023) recruited GBM via respondent-driven sampling in Montréal, Toronto, and Vancouver (n = 2449). We compared reported sexual partner distributions across cities and periods: before COVID-19 (2017-2019), pandemic (2020-2021), and after lifting of restrictions (2021-2023). We used Bayesian regression and poststratification to model partner distributions. We estimated mpox's basic reproduction number (R0) using a risk-stratified compartmental model. RESULTS: Pre-COVID-19 pandemic distributions were comparable: fitted average partners (past 6 months) were 10.4 (95% credible interval: 9.4-11.5) in Montréal, 13.1 (11.3-15.1) in Toronto, and 10.7 (9.5-12.1) in Vancouver. Sexual activity decreased during the pandemic and increased after lifting of restrictions, but remained below prepandemic levels. Based on reported cases, we estimated R0 of 2.4 to 2.7 and similar cumulative incidences (0.7%-0.9%) across cities. CONCLUSIONS: Similar sexual partner distributions may explain comparable R0 and cumulative incidence across cities. With potential for further recovery in sexual activity, mpox vaccination and surveillance strategies should be maintained.

Who acquires infection from whom? A sensitivity analysis of transmission dynamics during the early phase of the COVID-19 pandemic in Belgium.

Age-related heterogeneity in a host population, whether due to how individuals mix and contact each other, the nature of host-pathogen interactions defining epidemiological parameters, or demographics, is crucial in studying infectious disease dynamics. Compartmental models represent a popular approach to address the problem, dividing the population of interest into a discrete and finite number of states depending on, for example, individuals' age and stage of infection. We study the corresponding linearised system whose operator, in the context of a discrete-time model, equates to a square matrix known as the next generation matrix. Performing formal perturbation analysis of the entries of the aforementioned matrix, we derive indices to quantify the age-specific variation of its dominant eigenvalue (i.e., the reproduction number) and explore the relevant epidemiological information we can derive from the eigenstructure of the matrix. The resulting method enables the assessment of the impact of age-related population heterogeneity on virus transmission. In particular, starting from an age-structured SEIR model, we demonstrate the use of this approach for COVID-19 dynamics in Belgium. We analyse the early stages of the SARS-CoV-2 spread, with particular attention to the pre-pandemic framework and the lockdown lifting phase initiated as of May 2020. Our results, influenced by our assumption on age-specific susceptibility and infectiousness, support the hypothesis that transmission was only influenced to a small extent by children in the age group [0,18) and adults over 60 years of age during the early phases of the pandemic and up to the end of July 2020.

Optimal control of bi-seasonal hand, foot and mouth disease in mainland China suggests transmission from children and isolating older infected individuals are critical.

Hand, foot and mouth disease (HFMD) is a Class C infectious disease that carries particularly high risk for preschool children and is a leading cause of childhood death in some countries. We mimic the periodic outbreak of HFMD over a 2-year period-with differing amplitudes-and propose a dynamic HFMD model that differentiates transmission between mature and immature individuals and uses two possible optimal-control strategies to minimize case numbers, total costs and deaths. We parameterized the model by fitting it to HFMD data in mainland China from January 2011 to December 2018, and the basic reproduction number was estimated as 0.9599. Sensitivity analysis demonstrates that transmission between immature and mature individuals contributes substantially to new infections. Increasing the isolation rates of infectious individuals-particularly mature infectious individuals-could greatly reduce the outbreak risk and potentially eradicate the disease in a relatively short time period. It follows that we have a reasonable chance of controlling HFMD if we can reduce transmission in children under 7 and isolate older infectious individuals.

Evaluation of age-structured vaccination strategies for curbing the disease spread.

Age structure is one of the crucial factors in characterizing the heterogeneous epidemic transmission. Vaccination is regarded as an effective control measure for prevention and control epidemics. Due to the shortage of vaccine capacity during the outbreak of epidemics, how to design vaccination policy has become an urgent issue in suppressing the disease transmission. In this paper, we make an effort to propose an age-structured SVEIHR model with the disease-caused death to take account of dynamics of age-related vaccination policy for better understanding disease spread and control. We present an explicit expression of the basic reproduction number R 0 , which determines whether or not the disease persists, and then establish the existence and stability of endemic equilibria under certain conditions. Numerical simulations are illustrated to show that the age-related vaccination policy has a tremendous influence on curbing the disease transmission. Especially, vaccination of people over 65 is better than for people aged 21-65 in terms of rapid eradication of the disease in Italy.

Transmission dynamics of a reaction-advection-diffusion dengue fever model with seasonal developmental durations and intrinsic incubation periods.

In this paper, we propose a reaction-advection-diffusion dengue fever model with seasonal developmental durations and intrinsic incubation periods. Firstly, we establish the well-posedness of the model. Secondly, we define the basic reproduction number ℜ 0 for this model and show that ℜ 0 is a threshold parameter: if ℜ 0 < 1 , then the disease-free periodic solution is globally attractive; if ℜ 0 > 1 , the system is uniformly persistent. Thirdly, we study the global attractivity of the positive steady state when the spatial environment is homogeneous and the advection of mosquitoes is ignored. As an example, we use the model to investigate the dengue fever transmission case in Guangdong Province, China, and explore the impact of model parameters on ℜ 0 . Our findings indicate that ignoring seasonality may underestimate ℜ 0 . Additionally, the spatial heterogeneity of transmission may increase the risk of disease transmission, while the increase of seasonal developmental durations, intrinsic incubation periods and advection rates can all reduce the risk of disease transmission.

Threshold dynamics of a reaction-advection-diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity.

Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction-advection-diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number R 0 and show that the disease-free periodic solution is globally attractive when R 0 < 1 whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case when R 0 > 1 . Moreover, we find that R 0 is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.

Modelling phytoplankton-virus interactions: phytoplankton blooms and lytic virus transmission.

A dynamic reaction-diffusion model of four variables is proposed to describe the spread of lytic viruses among phytoplankton in a poorly mixed aquatic environment. The basic ecological reproductive index for phytoplankton invasion and the basic reproduction number for virus transmission are derived to characterize the phytoplankton growth and virus transmission dynamics. The theoretical and numerical results from the model show that the spread of lytic viruses effectively controls phytoplankton blooms. This validates the observations and experimental results of Emiliana huxleyi-lytic virus interactions. The studies also indicate that the lytic virus transmission cannot occur in a low-light or oligotrophic aquatic environment.

Final epidemic size of a two-community SIR model with asymmetric coupling.

Communities are commonly not isolated but interact asymmetrically with each other, allowing the propagation of infectious diseases within the same community and between different communities. To reveal the impact of asymmetrical interactions and contact heterogeneity on disease transmission, we formulate a two-community SIR epidemic model, in which each community has its contact structure while communication between communities occurs through temporary commuters. We derive an explicit formula for the basic reproduction number R 0 , give an implicit equation for the final epidemic size z, and analyze the relationship between them. Unlike the typical positive correlation between R 0 and z in the classic SIR model, we find a negatively correlated relationship between counterparts of our model deviating from homogeneous populations. Moreover, we investigate the impact of asymmetric coupling mechanisms on R 0 . The results suggest that, in scenarios with restricted movement of susceptible individuals within a community, R 0 does not follow a simple monotonous relationship, indicating that an unbending decrease in the movement of susceptible individuals may increase R 0 . We further demonstrate that network contacts within communities have a greater effect on R 0 than casual contacts between communities. Finally, we develop an epidemic model without restriction on the movement of susceptible individuals, and the numerical simulations suggest that the increase in human flow between communities leads to a larger R 0 .

Vector-borne disease models with Lagrangian approach.

We develop a multi-group and multi-patch model to study the effects of population dispersal on the spatial spread of vector-borne diseases across a heterogeneous environment. The movement of host and/or vector is described by Lagrangian approach in which the origin or identity of each individual stays unchanged regardless of movement. The basic reproduction number [Formula: see text] of the model is defined and the strong connectivity of the host-vector network is succinctly characterized by the residence times matrices of hosts and vectors. Furthermore, the definition and criterion of the strong connectivity of general infectious disease networks are given and applied to establish the global stability of the disease-free equilibrium. The global dynamics of the model system are shown to be entirely determined by its basic reproduction number. We then obtain several biologically meaningful upper and lower bounds on the basic reproduction number which are independent or dependent of the residence times matrices. In particular, the heterogeneous mixing of hosts and vectors in a homogeneous environment always increases the basic reproduction number. There is a substantial difference on the upper bound of [Formula: see text] between Lagrangian and Eulerian modeling approaches. When only host movement between two patches is concerned, the subdivision of hosts (more host groups) can lead to a larger basic reproduction number. In addition, we numerically investigate the dependence of the basic reproduction number and the total number of infected hosts on the residence times matrix of hosts, and compare the impact of different vector control strategies on disease transmission.

A hybrid Lagrangian-Eulerian model for vector-borne diseases.

In this paper, a multi-patch and multi-group vector-borne disease model is proposed to study the effects of host commuting (Lagrangian approach) and/or vector migration (Eulerian approach) on disease spread. We first define the basic reproduction number of the model, R 0 , which completely determines the global dynamics of the model system. Namely, if R 0 ≤ 1 , then the disease-free equilibrium is globally asymptotically stable, and if R 0 > 1 , then there exists a unique endemic equilibrium which is globally asymptotically stable. Then, we show that the basic reproduction number has lower and upper bounds which are independent of the host residence times matrix and the vector migration matrix. In particular, nonhomogeneous mixing of hosts and vectors in a homogeneous environment generally increases disease persistence and the basic reproduction number of the model attains its minimum when the distributions of hosts and vectors are proportional. Moreover, R 0 can also be estimated by the basic reproduction numbers of disconnected patches if the environment is homogeneous. The optimal vector control strategy is obtained for a special scenario. In the two-patch and two-group case, we numerically analyze the dependence of the basic reproduction number and the total number of infected people on the host residence times matrix and illustrate the optimal vector control strategy in homogeneous and heterogeneous environments.

Impact of ontogenic changes on the dynamics of a fungal crop disease model motivated by coffee leaf rust.

Ontogenic resistance has been described for many plant-pathogen systems. Conversely, coffee leaf rust, a major fungal disease that drastically reduces coffee production, exhibits a form of ontogenic susceptibility, with a higher infection risk for mature leaves. To take into account stage-dependent crop response to phytopathogenic fungi, we developed an SEIR-U epidemiological model, where U stands for spores, which differentiates between young and mature leaves. Based on this model, we also explored the impact of ontogenic resistance on the sporulation rate. We computed the basic reproduction number [Formula: see text], which classically determines the stability of the disease-free equilibrium. We identified forward and backward bifurcation cases. The backward bifurcation is generated by the high sporulation of young leaves compared to mature ones. In this case, when the basic reproduction number is less than one, the disease can persist. These results provide useful insights on the disease dynamics and its control. In particular, ontogenic resistance may require higher control efforts to eradicate the disease.

The impact of temperature, humidity and closing school on the mumps epidemic: a case study in the mainland of China.

BACKGROUND: To control resurging infectious diseases like mumps, it is necessary to resort to effective control and preventive measures. These measures include increasing vaccine coverage, providing the community with advice on how to reduce exposure, and closing schools. To justify such intervention, it is important to understand how well each of these measures helps to limit transmission. METHODS: In this paper, we propose a simple SEILR (susceptible-exposed-symptomatically infectious-asymptomatically infectious-recovered) model by using a novel transmission rate function to incorporate temperature, humidity, and closing school factors. This new transmission rate function allows us to verify the impact of each factor either separately or combined. Using reported mumps cases from 2004 to 2018 in the mainland of China, we perform data fitting and parameter estimation to evaluate the basic reproduction number  R 0 . As a wide range of one-dose measles, mumps, and rubella (MMR) vaccine programs in China started only in 2008, we use different vaccination proportions for the first Stage I period (from 2004 to 2008) and the second Stage II period (from 2009 to 2018). This allows us to verify the importance of higher vaccine coverage with a possible second dose of MMR vaccine. RESULTS: We find that the basic reproduction number  R 0  is generally between 1 and 3. We then use the Akaike Information Criteria to assess the extent to which each of the three factors contributed to the spread of mumps. The findings suggest that the impact of all three factors is substantial, with temperature having the most significant impact, followed by school opening and closing, and finally humidity. CONCLUSION: We conclude that the strategy of increasing vaccine coverage, changing micro-climate (temperature and humidity), and closing schools can greatly reduce mumps transmission.

SARS-CoV-2 incidence monitoring and statistical estimation of the basic and time-varying reproduction number at the early onset of the pandemic in 45 sub-Saharan African countries.

The world battled to defeat a novel coronavirus 2019 (SARS-CoV-2 or COVID-19), a respiratory illness that is transmitted from person to person through contacts with droplets from infected persons. Despite efforts to disseminate preventable messages and adoption of mitigation strategies by governments and the World Health Organization (WHO), transmission spread globally. An accurate assessment of the transmissibility of the coronavirus remained a public health priority for many countries across the world to fight this pandemic, especially at the early onset. In this paper, we estimated the transmission potential of COVID-19 across 45 countries in sub-Saharan Africa using three approaches, namely, [Formula: see text] based on (i) an exponential growth model (ii) maximum likelihood (ML) estimation and (iii) a time-varying basic reproduction number at the early onset of the pandemic. Using data from March 14, 2020, to May 10, 2020, sub-Saharan African countries were still grappling with COVID-19 at that point in the pandemic. The region's basic reproduction number ([Formula: see text]) was 1.89 (95% CI: 1.767 to 2.026) using the growth model and 1.513 (95% CI: 1.491 to 1.535) with the maximum likelihood method, indicating that, on average, infected individuals transmitted the virus to less than two secondary persons. Several countries, including Sudan ([Formula: see text]: 2.03), Ghana ([Formula: see text]: 1.87), and Somalia ([Formula: see text]: 1.85), exhibited high transmission rates. These findings highlighted the need for continued vigilance and the implementation of effective control measures to combat the pandemic in the region. It is anticipated that the findings in this study would not only function as a historical record of reproduction numbers during the COVID-19 pandemic in African countries, but can serve as a blueprint for addressing future pandemics of a similar nature.

The discrete-time Kermack-McKendrick model: A versatile and computationally attractive framework for modeling epidemics.

The COVID-19 pandemic has led to numerous mathematical models for the spread of infection, the majority of which are large compartmental models that implicitly constrain the generation-time distribution. On the other hand, the continuous-time Kermack-McKendrick epidemic model of 1927 (KM27) allows an arbitrary generation-time distribution, but it suffers from the drawback that its numerical implementation is rather cumbersome. Here, we introduce a discrete-time version of KM27 that is as general and flexible, and yet is very easy to implement computationally. Thus, it promises to become a very powerful tool for exploring control scenarios for specific infectious diseases such as COVID-19. To demonstrate this potential, we investigate numerically how the incidence-peak size depends on model ingredients. We find that, with the same reproduction number and the same initial growth rate, compartmental models systematically predict lower peak sizes than models in which the latent and the infectious period have fixed duration.

Dynamical Analysis of an Improved Bidirectional Immunization SIR Model in Complex Network.

In order to investigate the impact of two immunization strategies-vaccination targeting susceptible individuals to reduce their infection rate and clinical medical interventions targeting infected individuals to enhance their recovery rate-on the spread of infectious diseases in complex networks, this study proposes a bilinear SIR infectious disease model that considers bidirectional immunization. By analyzing the conditions for the existence of endemic equilibrium points, we derive the basic reproduction numbers and outbreak thresholds for both homogeneous and heterogeneous networks. The epidemic model is then reconstructed and extensively analyzed using continuous-time Markov chain (CTMC) methods. This analysis includes the investigation of transition probabilities, transition rate matrices, steady-state distributions, and the transition probability matrix based on the embedded chain. In numerical simulations, a notable concordance exists between the outcomes of CTMC and mean-field (MF) simulations, thereby substantiating the efficacy of the CTMC model. Moreover, the CTMC-based model adeptly captures the inherent stochastic fluctuation in the disease transmission, which is consistent with the mathematical properties of Markov chains. We further analyze the relationship between the system's steady-state infection density and the immunization rate through MCS. The results suggest that the infection density decreases with an increase in the immunization rate among susceptible individuals. The current research results will enhance our understanding of infectious disease transmission patterns in real-world scenarios, providing valuable theoretical insights for the development of epidemic prevention and control strategies.

Quantifying Mycobacterium tuberculosis Transmission Dynamics Across Global Settings: A Systematic Analysis.

The degree to which individual heterogeneity in the production of secondary cases ("superspreading") affects tuberculosis (TB) transmission has not been systematically studied. We searched for population-based or surveillance studies in which whole genome sequencing was used to estimate TB transmission and in which the size distributions of putative TB transmission clusters were enumerated. We fitted cluster-size-distribution data to a negative binomial branching process model to jointly infer the transmission parameters $R$ (the reproduction number) and the dispersion parameter, $k$, which quantifies the propensity of superspreading in a population (generally, lower values of $k$ ($<1.0$) suggest increased heterogeneity). Of 4,796 citations identified in our initial search, 9 studies from 8 global settings met the inclusion criteria (n = 5 studies of all TB; n = 4 studies of drug-resistant TB). Estimated $R$ values (range, 0.10-0.73) were below 1.0, consistent with declining epidemics in the included settings; estimated $k$ values were well below 1.0 (range, 0.02-0.48), indicating the presence of substantial individual-level heterogeneity in transmission across all settings. We estimated that a minority of cases (range, 2%-31%) drive the majority (80%) of ongoing TB transmission at the population level. Identifying sources of heterogeneity and accounting for them in TB control may have a considerable impact on mitigating TB transmission.

Transmissibility quantification of norovirus outbreaks in 2016-2021 in Beijing, China.

The transmissibility is a crucial feature for norovirus, yet its quantitative estimation has been limited. Our objective was to estimate the basic reproduction number (R0 ) of norovirus and investigate its variation characteristics. Norovirus outbreaks reported from September 2016 to August 2021 in Beijing were analyzed. The susceptible-infected-removed compartment model was established to estimate R0 . Linear regression models and logistic regression models were used to explore the factors affecting the transmissibility of norovirus. The overall median R0 of norovirus was estimated as 2.1 (interquartile range [IQR] 1.8-2.5), with 650 norovirus outbreaks. The transmissibility of norovirus varied by year, outbreak setting and genotype. The R0 of norovirus during September 2019 to August 2020 (median 2.1, IQR 1.8-2.4) and September 2020 to August 2021 (median 2.0, IQR 1.7-2.3) was lower than that of September 2016 to August 2017 (median 2.3, IQR 1.8-2.7) (ß = 0.94, p = 0.05; ß = 0.93, p = 0.008). The R0 of norovirus for all other settings was lower than that for kindergarten (median 2.4, IQR 2.0-2.9) (primary school: median 2.0, IQR 1.7-2.4, ß = 0.94, p = 0.001; secondary school: median 1.7, IQR 1.5-2.0, ß = 0.87, p < 0.001; college: median 1.7, IQR 1.5-1.8, ß = 0.89, p = 0.03; other closed settings: median 1.8, IQR 1.5-2.0, ß = 0.90, p = 0.004). GⅡ.2[P16] outbreaks had a median R0 of 2.2 (IQR 1.8-2.7), which was higher than that for GⅡ.6[P7] outbreaks (median 1.8, IQR: 1.8-2.0, odds ratio = 0.19, p = 0.03; GⅡ.2[P16] as reference) and mixed-genotype outbreaks (median 1.7, IQR: 1.5-1.8, ß = 0.92, p = 0.02; mixed-genotype as reference). In kindergartens and primary schools, norovirus shows increased transmissibility, emphasizing the vulnerable population and high-risk settings. Furthermore, the transmissibility of norovirus may change over time and with virus evolution, necessitating additional research to uncover the underlying mechanisms.

Adaptive changes in sexual behavior in the high-risk population in response to human monkeypox transmission in Canada can help control the outbreak: Insights from a two-group, two-route epidemic model.

Monkeypox, a zoonotic disease, is emerging as a potential sexually transmitted infection/disease, with underlying transmission mechanisms still unclear. We devised a risk-structured, compartmental model, incorporating sexual behavior dynamics. We compared different strategies targeting the high-risk population: a scenario of control policies geared toward the use of condoms and/or sexual abstinence (robust control strategy) with risk compensation behavior change, and a scenario of control strategies with behavior change in response to the doubling rate (adaptive control strategy). Monkeypox's basic reproduction number is 1.464, 0.0066, and 1.461 in the high-risk, low-risk, and total populations, respectively, with the high-risk group being the major driver of monkeypox spread. Policies imposing condom use or sexual abstinence need to achieve a 35% minimum compliance rate to stop further transmission, while a combination of both can curb the spread with 10% compliance to abstinence and 25% to condom use. With risk compensation, the only option is to impose sexual abstinence by at least 35%. Adaptive control is more effective than robust control where the daily sexual contact number is reduced proportionally and remains constant thereafter, shortening the time to epidemic peak, lowering its size, facilitating disease attenuation, and playing a key role in controlling the current outbreak.

The global asymptotical stability of pseudorabies model with age-structure.

In this paper, the dynamics of an infectious disease is studied by considering age-structured models; a stage structure and an age-structured epidemic model. The respective basic reproduction numbers for the proposed models are calculated, and the local analyses of the equilibria of the models are investigated by using the method of linearization. The global dynamics of the two models are analyzed by using the wave lemma and the Lyapunov function theory. This study establishes a solid theoretical framework and a rigorous mathematical formulation for the prevention and control of pseudorabies.