Instabilities and self-organization in spatiotemporal epidemic dynamics driven by nonlinearity and noise.

Theoretical analysis of epidemic dynamics has attracted significant attention in the aftermath of the COVID-19 pandemic. In this article, we study dynamic instabilities in a spatiotemporal compartmental epidemic model represented by a stochastic system of coupled partial differential equations (SPDE). Saturation effects in infection spread-anchored in physical considerations-lead to strong nonlinearities in the SPDE. Our goal is to study the onset of dynamic, Turing-type instabilities, and the concomitant emergence of steady-state patterns under the interplay between three critical model parameters-the saturation parameter, the noise intensity, and the transmission rate. Employing a second-order perturbation analysis to investigate stability, we uncover both diffusion-driven and noise-induced instabilities and corresponding self-organized distinct patterns of infection spread in the steady state. We also analyze the effects of the saturation parameter and the transmission rate on the instabilities and the pattern formation. In summary, our results indicate that the nuanced interplay between the three parameters considered has a profound effect on the emergence of dynamical instabilities and therefore on pattern formation in the steady state. Moreover, due to the central role played by the Turing phenomenon in pattern formation in a variety of biological dynamic systems, the results are expected to have broader significance beyond epidemic dynamics.

Source-Sink Dynamics in a Two-Patch SI Epidemic Model with Life Stages and No Recovery from Infection.

This study presents a comprehensive analysis of a two-patch, two-life stage SI model without recovery from infection, focusing on the dynamics of disease spread and host population viability in natural populations. The model, inspired by real-world ecological crises like the decline of amphibian populations due to chytridiomycosis and sea star populations due to Sea Star Wasting Disease, aims to understand the conditions under which a sink host population can present ecological rescue from a healthier, source population. Mathematical and numerical analyses reveal the critical roles of the basic reproductive numbers of the source and sink populations, the maturation rate, and the dispersal rate of juveniles in determining population outcomes. The study identifies basic reproduction numbers R 0 for each of the patches, and conditions for the basic reproduction numbers to produce a receiving patch under which its population. These findings provide insights into managing natural populations affected by disease, with implications for conservation strategies, such as the importance of maintaining reproductively viable refuge populations and considering the effects of dispersal and maturation rates on population recovery. The research underscores the complexity of host-pathogen dynamics in spatially structured environments and highlights the need for multi-faceted approaches to biodiversity conservation in the face of emerging diseases.

Studying the impacts of variant evolution for a generalized age-group transmission model.

The differences of SARS-CoV-2 variants brought the changes of transmission characteristics and clinical manifestations during the prevalence of COVID-19. In order to explore the evolution mechanisms of SARS-CoV-2 variants and the impacts of variant evolution, the classic SIR (Susceptible-Infected-Recovered) compartment model was modified to a generalized SVEIR (Susceptible-Vaccinated-Exposed-Infected-Recovered) compartment model with age-group and varying variants in this study. By using of the SVEIR model and least squares method, the optimal fittings against the surveillance data from Fujian Provincial Center for Disease Control and Prevention were performed for the five epidemics of Fujian Province. The main epidemiological characteristics such as basic reproduction number, effective reproduction number, sensitivity analysis, and cross-variant scenario investigations were extensively investigated during dynamic zero-COVID policy. The study results showed that the infectivities of the variants became fast from wild strain to the Delta variant, further to the Omicron variant. Meanwhile, the cross-variant investigations showed that the average incubation periods were shortened, and that the infection scales quickly enhanced. Further, the risk estimations with the new variants were performed without implements of the non-pharmaceutical interventions, based on the dominant variants XBB.1.9.1 and EG.5. The results of the risk estimations suggested that non-pharmaceutical interventions were necessary on the Chinese mainland for controlling severe infections and deaths, and also that the regular variant monitors were still workable against the aggressive variant evolution and the emergency of new transmission risks in the future.

Prevention and control of Ebola virus transmission: mathematical modelling and data fitting.

The Ebola virus disease (EVD) has been endemic since 1976, and the case fatality rate is extremely high. EVD is spread by infected animals, symptomatic individuals, dead bodies, and contaminated environment. In this paper, we formulate an EVD model with four transmission modes and a time delay describing the incubation period. Through dynamical analysis, we verify the importance of blocking the infection source of infected animals. We get the basic reproduction number without considering the infection source of infected animals. And, it is proven that the model has a globally attractive disease-free equilibrium when the basic reproduction number is less than unity; the disease eventually becomes endemic when the basic reproduction number is greater than unity. Taking the EVD epidemic in Sierra Leone in 2014-2016 as an example, we complete the data fitting by combining the effect of the media to obtain the unknown parameters, the basic reproduction number and its time-varying reproduction number. It is shown by parameter sensitivity analysis that the contact rate and the removal rate of infected group have the greatest influence on the prevalence of the disease. And, the disease-controlling thresholds of these two parameters are obtained. In addition, according to the existing vaccination strategy, only the inoculation ratio in high-risk areas is greater than 0.4, the effective reproduction number can be less than unity. And, the earlier the vaccination time, the greater the inoculation ratio, and the faster the disease can be controlled.

Bayesian inference for the onset time and epidemiological characteristics of emerging infectious diseases.

Background: Emerging infectious diseases pose a significant threat to global public health. Timely detection and response are crucial in mitigating the spread of such epidemics. Inferring the onset time and epidemiological characteristics is vital for accelerating early interventions, but accurately predicting these parameters in the early stages remains challenging. Methods: We introduce a Bayesian inference method to fit epidemic models to time series data based on state-space modeling, employing a stochastic Susceptible-Exposed-Infectious-Removed (SEIR) model for transmission dynamics analysis. Our approach uses the particle Markov chain Monte Carlo (PMCMC) method to estimate key epidemiological parameters, including the onset time, the transmission rate, and the recovery rate. The PMCMC algorithm integrates the advantageous aspects of both MCMC and particle filtering methodologies to yield a computationally feasible and effective means of approximating the likelihood function, especially when it is computationally intractable. Results: To validate the proposed method, we conduct case studies on COVID-19 outbreaks in Wuhan, Shanghai and Nanjing, China, respectively. Using early-stage case reports, the PMCMC algorithm accurately predicted the onset time, key epidemiological parameters, and the basic reproduction number. These findings are consistent with empirical studies and the literature. Conclusion: This study presents a robust Bayesian inference method for the timely investigation of emerging infectious diseases. By accurately estimating the onset time and essential epidemiological parameters, our approach is versatile and efficient, extending its utility beyond COVID-19.

Dynamics of simplicial SEIRS epidemic model: global asymptotic stability and neural Lyapunov functions.

The transmission of infectious diseases on a particular network is ubiquitous in the physical world. Here, we investigate the transmission mechanism of infectious diseases with an incubation period using a networked compartment model that contains simplicial interactions, a typical high-order structure. We establish a simplicial SEIRS model and find that the proportion of infected individuals in equilibrium increases due to the many-body connections, regardless of the type of connections used. We analyze the dynamics of the established model, including existence and local asymptotic stability, and highlight differences from existing models. Significantly, we demonstrate global asymptotic stability using the neural Lyapunov function, a machine learning technique, with both numerical simulations and rigorous analytical arguments. We believe that our model owns the potential to provide valuable insights into transmission mechanisms of infectious diseases on high-order network structures, and that our approach and theory of using neural Lyapunov functions to validate model asymptotic stability can significantly advance investigations on complex dynamics of infectious disease.

Evolutionary Invasion Analysis of Modern Epidemics Highlights the Context-Dependence of Virulence Evolution.

Models are often employed to integrate knowledge about epidemics across scales and simulate disease dynamics. While these approaches have played a central role in studying the mechanics underlying epidemics, we lack ways to reliably predict how the relationship between virulence (the harm to hosts caused by an infection) and transmission will evolve in certain virus-host contexts. In this study, we invoke evolutionary invasion analysis-a method used to identify the evolution of uninvadable strategies in dynamical systems-to examine how the virulence-transmission dichotomy can evolve in models of virus infections defined by different natural histories. We reveal peculiar patterns of virulence evolution between epidemics with different disease natural histories (SARS-CoV-2 and hepatitis C virus). We discuss the findings with regards to the public health implications of predicting virus evolution, and in broader theoretical canon involving virulence evolution in host-parasite systems.

Impact assessment of self-medication on COVID-19 prevalence in Gauteng, South Africa, using an age-structured disease transmission modelling framework.

OBJECTIVE: To assess the impact of self-medication on the transmission dynamics of COVID-19 across different age groups, examine the interplay of vaccination and self-medication in disease spread, and identify the age group most prone to self-medication. METHODS: We developed an age-structured compartmentalized epidemiological model to track the early dynamics of COVID-19. Age-structured data from the Government of Gauteng, encompassing the reported cumulative number of cases and daily confirmed cases, were used to calibrate the model through a Markov Chain Monte Carlo (MCMC) framework. Subsequently, uncertainty and sensitivity analyses were conducted on the model parameters. RESULTS: We found that self-medication is predominant among the age group 15-64 (74.52%), followed by the age group 0-14 (34.02%), and then the age group 65+ (11.41%). The mean values of the basic reproduction number, the size of the first epidemic peak (the highest magnitude of the disease), and the time of the first epidemic peak (when the first highest magnitude occurs) are 4.16499, 241,715 cases, and 190.376 days, respectively. Moreover, we observed that self-medication among individuals aged 15-64 results in the highest spreading rate of COVID-19 at the onset of the outbreak and has the greatest impact on the first epidemic peak and its timing. CONCLUSION: Studies aiming to understand the dynamics of diseases in areas prone to self-medication should account for this practice. There is a need for a campaign against COVID-19-related self-medication, specifically targeting the active population (ages 15-64).

SIR+ models: accounting for interaction-dependent disease susceptibility in the planning of public health interventions.

Avoiding physical contact is regarded as one of the safest and most advisable strategies to follow to reduce pathogen spread. The flip side of this approach is that a lack of social interactions may negatively affect other dimensions of health, like induction of immunosuppressive anxiety and depression or preventing interactions of importance with a diversity of microbes, which may be necessary to train our immune system or to maintain its normal levels of activity. These may in turn negatively affect a population's susceptibility to infection and the incidence of severe disease. We suggest that future pandemic modelling may benefit from relying on 'SIR+ models': epidemiological models extended to account for the benefits of social interactions that affect immune resilience. We develop an SIR+ model and discuss which specific interventions may be more effective in balancing the trade-off between minimizing pathogen spread and maximizing other interaction-dependent health benefits. Our SIR+ model reflects the idea that health is not just the mere absence of disease, but rather a state of physical, mental and social well-being that can also be dependent on the same social connections that allow pathogen spread, and the modelling of public health interventions for future pandemics should account for this multidimensionality.

Based on epidemiological parameter data, probe into a stochastically perturbed dominant variant of the COVID-19 pandemic model.

During the COVID-19 pandemic, the SARS-CoV-2 gene mutation has been rapidly emerging and spreading all over the world. Experts worldwide regularly monitor genetic mutations and variants through genome-sequence-based surveillance, laboratory testing, outbreak investigation, and epidemiological probing. Clinical pathologists and medical laboratory scientists prefer developing or endorsing COVID-19 vaccines with a broader immune response involving various antibodies and cells to protect against mutations or new variants. Randomness plays an enormous role in pathology and epidemiology. Hence, based on epidemiological parameter data, we construct and probe a stochastically perturbed dominant variant of the coronavirus epidemic model with three nonlinear saturated incidence rates. We reveal the existence of a unique global positive solution to the constructed stochastic COVID-19 model. The Lyapunov function method is used to determine the presence of a stationary distribution of positive solutions. We derive sufficient conditions for the coronavirus to be eradicated. Eventually, numerical simulations validate the effectiveness of our theoretical outcomes.

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.

An SEIR network epidemic model with manual and digital contact tracing allowing delays.

We consider an SEIR epidemic model on a network also allowing random contacts, where recovered individuals could either recover naturally or be diagnosed. Upon diagnosis, manual contact tracing is triggered such that each infected network contact is reported, tested and isolated with some probability and after a random delay. Additionally, digital tracing (based on a tracing app) is triggered if the diagnosed individual is an app-user, and then all of its app-using infectees are immediately notified and isolated. The early phase of the epidemic with manual and/or digital tracing is approximated by different multi-type branching processes, and three respective reproduction numbers are derived. The effectiveness of both contact tracing mechanisms is numerically quantified through the reduction of the reproduction number. This shows that app-using fraction plays an essential role in the overall effectiveness of contact tracing. The relative effectiveness of manual tracing compared to digital tracing increases if: more of the transmission occurs on the network, when the tracing delay is shortened, and when the network degree distribution is heavy-tailed. For realistic values, the combined tracing case can reduce R0 by 20%-30%, so other preventive measures are needed to reduce the reproduction number down to 1.2-1.4 for contact tracing to make it successful in avoiding big outbreaks.

JAGS model specification for spatiotemporal epidemiological modelling.

Bayesian inference in modelling infectious diseases using Bayesian inference using Gibbs Sampling (BUGS) is notable in the last two decades in parallel with the advancements in computing and model development. The ability of BUGS to easily implement the Markov chain Monte Carlo (MCMC) method brought Bayesian analysis to the mainstream of infectious disease modelling. However, with the existing software that runs MCMC to make Bayesian inferences, it is challenging, especially in terms of computational complexity, when infectious disease models become more complex with spatial and temporal components, in addition to the increasing number of parameters and large datasets. This study investigates two alternative subscripting strategies for creating models in Just Another Gibbs Sampler (JAGS) environment and their performance in terms of run times. Our results are useful for practitioners to ensure the efficiency and timely implementation of Bayesian spatiotemporal infectious disease modelling.

An SIS epidemic model with individual variation.

We study an extension of the stochastic SIS (Susceptible-Infectious-Susceptible) model in continuous time that accounts for variation amongst individuals. By examining its limiting behaviour as the population size grows we are able to exhibit conditions for the infection to become endemic.

Estimating time-varying epidemiological parameters and underreporting of Covid-19 cases in Brazil using a mathematical model with fuzzy transitions between epidemic periods.

Our study conducts a comprehensive analysis of the Covid-19 pandemic in Brazil, spanning five waves over three years. We employed a novel Susceptible-Infected-Recovered-Dead-Susceptible (SIRDS) model with a fuzzy transition between epidemic periods to estimate time-varying parameters and evaluate case underreporting. The initial basic reproduction number (R0) is identified at 2.44 (95% Confidence Interval (CI): 2.42-2.46), decreasing to 1.00 (95% CI: 0.99-1.01) during the first wave. The model estimates an underreporting factor of 12.9 (95% CI: 12.5-13.2) more infections than officially reported by Brazilian health authorities, with an increasing factor of 5.8 (95% CI: 5.2-6.4), 12.9 (95% CI: 12.5-13.3), and 16.8 (95% CI: 15.8-17.5) in 2020, 2021, and 2022 respectively. Additionally, the Infection Fatality Rate (IFR) is initially 0.88% (95% CI: 0.81%-0.94%) during the initial phase but consistently reduces across subsequent outbreaks, reaching its lowest value of 0.018% (95% CI: 0.011-0.033) in the last outbreak. Regarding the immunity period, the observed uncertainty and low sensitivity indicate that inferring this parameter is particularly challenging. Brazil successfully reduced R0 during the first wave, coinciding with decreased human mobility. Ineffective public health measures during the second wave resulted in the highest mortality rates within the studied period. We attribute lower mortality rates in 2022 to increased vaccination coverage and the lower lethality of the Omicron variant. We demonstrate the model generalization by its application to other countries. Comparative analyses with serological research further validate the accuracy of the model. In forecasting analysis, our model provides reasonable outbreak predictions. In conclusion, our study provides a nuanced understanding of the Covid-19 pandemic in Brazil, employing a novel epidemiological model. The findings contribute to the broader discourse on pandemic dynamics, underreporting, and the effectiveness of health interventions.

Mathematical Assessment of the Role of Human Behavior Changes on SARS-CoV-2 Transmission Dynamics in the United States.

The COVID-19 pandemic has not only presented a major global public health and socio-economic crisis, but has also significantly impacted human behavior towards adherence (or lack thereof) to public health intervention and mitigation measures implemented in communities worldwide. This study is based on the use of mathematical modeling approaches to assess the extent to which SARS-CoV-2 transmission dynamics is impacted by population-level changes of human behavior due to factors such as (a) the severity of transmission (such as disease-induced mortality and level of symptomatic transmission), (b) fatigue due to the implementation of mitigation interventions measures (e.g., lockdowns) over a long (extended) period of time, (c) social peer-pressure, among others. A novel behavior-epidemiology model, which takes the form of a deterministic system of nonlinear differential equations, is developed and fitted using observed cumulative SARS-CoV-2 mortality data during the first wave in the United States. The model fits the observed data, as well as makes a more accurate prediction of the observed daily SARS-CoV-2 mortality during the first wave (March 2020-June 2020), in comparison to the equivalent model which does not explicitly account for changes in human behavior. This study suggests that, as more newly-infected individuals become asymptomatically-infectious, the overall level of positive behavior change can be expected to significantly decrease (while new cases may rise, particularly if asymptomatic individuals have higher contact rate, in comparison to symptomatic individuals).

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.

Future malaria environmental suitability in Africa is sensitive to hydrology.

Changes in climate shift the geographic locations that are suitable for malaria transmission because of the thermal constraints on vector Anopheles mosquitos and Plasmodium spp. malaria parasites and the lack of availability of surface water for vector breeding. Previous Africa-wide assessments have tended to solely represent surface water using precipitation, ignoring many important hydrological processes. Here, we applied a validated and weighted ensemble of global hydrological and climate models to estimate present and future areas of hydroclimatic suitability for malaria transmission. With explicit surface water representation, we predict a net decrease in areas suitable for malaria transmission from 2025 onward, greater sensitivity to future greenhouse gas emissions, and different, more complex, malaria transmission patterns. Areas of malaria transmission that are projected to change are smaller than those estimated by precipitation-based estimates but are associated with greater changes in transmission season lengths.

Importance of social inequalities to contact patterns, vaccine uptake, and epidemic dynamics.

Individuals' socio-demographic and economic characteristics crucially shape the spread of an epidemic by largely determining the exposure level to the virus and the severity of the disease for those who got infected. While the complex interplay between individual characteristics and epidemic dynamics is widely recognised, traditional mathematical models often overlook these factors. In this study, we examine two important aspects of human behaviour relevant to epidemics: contact patterns and vaccination uptake. Using data collected during the COVID-19 pandemic in Hungary, we first identify the dimensions along which individuals exhibit the greatest variation in their contact patterns and vaccination uptake. We find that generally higher socio-economic groups of the population have a higher number of contacts and a higher vaccination uptake with respect to disadvantaged groups. Subsequently, we propose a data-driven epidemiological model that incorporates these behavioural differences. Finally, we apply our model to analyse the fourth wave of COVID-19 in Hungary, providing valuable insights into real-world scenarios. By bridging the gap between individual characteristics and epidemic spread, our research contributes to a more comprehensive understanding of disease dynamics and informs effective public health strategies.

Conventional and frugal methods of estimating COVID-19-related excess deaths and undercount factors.

Across the world, the officially reported number of COVID-19 deaths is likely an undercount. Establishing true mortality is key to improving data transparency and strengthening public health systems to tackle future disease outbreaks. In this study, we estimated excess deaths during the COVID-19 pandemic in the Pune region of India. Excess deaths are defined as the number of additional deaths relative to those expected from pre-COVID-19-pandemic trends. We integrated data from: (a) epidemiological modeling using pre-pandemic all-cause mortality data, (b) discrepancies between media-reported death compensation claims and official reported mortality, and (c) the "wisdom of crowds" public surveying. Our results point to an estimated 14,770 excess deaths [95% CI 9820-22,790] in Pune from March 2020 to December 2021, of which 9093 were officially counted as COVID-19 deaths. We further calculated the undercount factor-the ratio of excess deaths to officially reported COVID-19 deaths. Our results point to an estimated undercount factor of 1.6 [95% CI 1.1-2.5]. Besides providing similar conclusions about excess deaths estimates across different methods, our study demonstrates the utility of frugal methods such as the analysis of death compensation claims and the wisdom of crowds in estimating excess mortality.