Disease Transmission Model Research Articles

Path Integral Control in Infectious Disease Modeling

Path Integral Control in Infectious Disease Modeling

Dynamics and analysis of COVID-19 disease transmission: The effect of vaccination and quarantine

<abstract><p>In this study, a fractional-order model for COVID-19 disease transmission is proposed and studied. First, the disease-free equilibrium and the basic reproduction number, $ {\cal R}_0 $ of the model has been communicated. The local and global stability of the disease-free equilibrium have been proved using well-constructed Lyapunov functions. Moreover, a normalized sensitivity analysis for the model parameters has been performed to identify their influence on $ {\cal R}_0 $. Real data on COVID-19 disease from Wuhan in China has been used to validate the proposed model. Finally, a simulation of the model has been performed to determine the effects of memory and control strategies. Overall, one can note that vaccination and quarantine have the potential to minimize the spread of COVID-19 in the population.</p></abstract>

Dynamics of plant disease models with continuous and pulse farming awareness control

<p style='text-indent:20px;'>How to develop the mathematical model of plant disease transmission and consider the effect of saturated farming awareness strategies on plant disease control is of great practical significance. To do this, the plant disease transmission models with continuous and pulse farming awareness control strategy have been proposed in the present paper. For the model with continuous control strategies, the threshold values for the existence and stability of multiple equilibria have been given, and the effect of farming awareness on disease persistence is discussed; For the model with nonlinear impulsive control tactics, the existence and stability of the plant disease-free periodic solutions are investigated and the threshold condition is given, further we get the conditions for the permanence of the system and obtain the sufficient conditions under which the positive periodic solution exists by bifurcation theory. Numerical simulations reveal that people's farming awareness, especially global awareness, plays an important role in controlling and eradicating the plant disease. Moreover, the nonlinear impulsive control could result in the complex dynamic behavior, including period doubling, chaos and multiple attractors, which makes it difficult to design a successful plant disease control strategy.</p>

Markov modeling and performance analysis of infectious diseases with asymptomatic patients.

After over three years of COVID-19, it has become clear that infectious diseases are difficult to eradicate, and humans remain vulnerable under their influence in a long period. The presence of presymptomatic and asymptomatic patients is a significant obstacle to preventing and eliminating infectious diseases. However, the long-term transmission of infectious diseases involving asymptomatic patients still remains unclear. To address this issue, this paper develops a novel Markov process for infectious diseases with asymptomatic patients by means of a continuous-time level-dependent quasi-birth-and-death (QBD) process. The model accurately captures the transmission of infectious diseases by specifying several key parameters (or factors). To analyze the role of asymptomatic and symptomatic patients in the infectious disease transmission process, a simple sufficient condition for the stability of the Markov process of infectious diseases is derived using the mean drift technique. Then, the stationary probability vector of the QBD process is obtained by using RG-factorizations. A method of using the stationary probability vector is provided to obtain important performance measures of the model. Finally, some numerical experiments are presented to demonstrate the model's feasibility through analyzing COVID-19 as an example. The impact of key parameters on the system performance evaluation and the infectious disease transmission process are analyzed. The methodology and results of this paper can provide theoretical and technical support for the scientific control of the long-term transmission of infectious diseases, and we believe that they can serve as a foundation for developing more general models of infectious disease transmission.

Optimal Combinations of Control Strategies and Cost-Effectiveness Analysis of Dynamics of Endemic Malaria Transmission Model.

In this study, we propose and analyze a determinastic nonlinear system of ordinary differential equation model for endemic malaria disease transmission and optimal combinations of control strategies with cost effective analysis. Basic properties of the model, existence of disease-free and endemic equilibrium points, and basic reproduction number of the model are derived and analyzed. From this analysis, we conclude that if the basic reproduction number is less than unity, then the disease-free equilibrium point is both locally and globally asymptotically stable. The endemic equilibrium will also exist if the basic reproduction number is greater than unity. Moreover, existence and necessary condition for forward bifurcation is derived and established. Furthermore, optimal combinations of time-dependent control measures are incorporated to the model. By using Pontryagin's maximum principal theory, we derived the necessary conditions of optimal control. Numerical simulations were conducted to confirm our analytical results. Our findings were that malaria disease may be controlled well with strict application of the combination of prevention of drug resistance, insecticide-treated net (ITN), indoor residual spray (IRS), and active treatment. The use of a combination of insecticide-treated net, indoor residual spray, and active treatment is the most optimal cost-effective and efficacious strategy.

Optimal control of a tick population with a view to control of Rocky Mountain Spotted Fever.

In some regions of the Americas, domestic dogs are the host for the tick vector Rhipicephalus sanguineus, and spread the tick-borne pathogen Rickettsia rickettsii, which causes Rocky Mountain Spotted Fever (RMSF) in humans. Interventions are carried out against the vector via dog collars and acaricidal wall treatments. This paper investigates the optimal control of acaricidal wall treatments, using a prior model for populations and disease transmission developed for this particular vector, host, and pathogen. It is modified with a death term during questing stages reflecting the cost of control and level of coverage. In the presence of the control, the percentage of dogs and ticks infected with Ri. rickettsii decreases in a short period and remains suppressed for a longer period, including after treatment is discontinued. Risk of RMSF infection declines by 90% during this time. In the absence of re-application, infected tick and dog populations rebound, indicating the eventual need for repeated treatment.

Mathematical model for soybean mosaic disease transmission with entomopathogen interventions and photoperiodicity

Mosaic is a severe disease of soybeans that has the potential to reduce the quality and quantity of soybean production. The Mosaic disease can infect soybean plants by the Aphis vector carrying Soybean Mosaic Virus (SMV). In this study, a mathematical model of the spread of Mosaic disease was built by considering two interventions, namely the application of entomopathogen and the regulation of photosynthesis intensity. This research focuses on knowing the effect of intervention in controlling Mosaic disease and increasing the population of susceptible generative plants. Using dynamical system theory, non-endemic and endemic equilibrium points and their stability are obtained. Then, the basic reproduction ratio (R0) is obtained for this model. Sensitivity analysis was carried out to determine the most influential parameters in the model. Optimal control theory was used to determine the optimal conditions of the model by considering the cost of entomopathogen application and photoperiodicity. The results of numerical simulations show that the application of entomopathogen and photosynthetic intensity can suppress the population of plant and vector infections and increase the population of susceptible plants in the generative phase at the same time.

Effects of Contact Tracing and Self-Reporting in a Network Disease Model

Contact tracing can be an effective measure to control emerging infectious diseases, but the efficacy of contact tracing measures can depend upon the willingness of individuals to get be tested even when they are symptomatic. In this paper, we examine the effects of symptomatic individuals getting tested and the use of contact tracing in a network model of disease transmission. We utilize a network model to resolve the influence of contact patterns between individuals as apposed to assuming mass action where all individuals are connected to each other.  We find that the effects of self-reporting and contact tracing vary depending on the structure of the network. We also compare the results from the network model with an analogous ODE model that assumes mass action and demonstrate how the results can be dramatically different.

Social divisions and risk perception drive divergent epidemics and large later waves.

During infectious disease outbreaks, individuals may adopt protective measures like vaccination and physical distancing in response to awareness of disease burden. Prior work showed how feedbacks between epidemic intensity and awareness-based behaviour shape disease dynamics. These models often overlook social divisions, where population subgroups may be disproportionately impacted by a disease and more responsive to the effects of disease within their group. We develop a compartmental model of disease transmission and awareness-based protective behaviour in a population split into two groups to explore the impacts of awareness separation (relatively greater in- vs. out-group awareness of epidemic severity) and mixing separation (relatively greater in- vs. out-group contact rates). Using simulations, we show that groups that are more separated in awareness have smaller differences in mortality. Fatigue (i.e. abandonment of protective measures over time) can drive additional infection waves that can even exceed the size of the initial wave, particularly if uniform awareness drives early protection in one group, leaving that group largely susceptible to future infection. Counterintuitively, vaccine or infection-acquired immunity that is more protective against transmission and mortality may indirectly lead to more infections by reducing perceived risk of infection and therefore vaccine uptake. Awareness-based protective behaviour, including awareness separation, can fundamentally alter disease dynamics. Social media summary: Depending on group division, behaviour based on perceived risk can change epidemic dynamics & produce large later waves.

Incorporating Heterogeneity in Farmer Disease Control Behaviour into a Livestock Disease Transmission Model

Incorporating Heterogeneity in Farmer Disease Control Behaviour into a Livestock Disease Transmission Model

GANs for Privacy-Aware Mobility Modeling

Human mobility modeling is crucial for many facets of our society, including disease transmission modeling and urban planning. The explosion of mobility data prompted the application of deep learning to human mobility. Along with the growth of research interest, there is also increasing privacy concern. This study first examines the cutting-edge approaches for trajectory generation, classification, and next-location prediction. Second, we propose a novel privacy-aware approach for predicting next-week trajectories. The approach is based on two modules, a Generative Adversarial Network used for generating synthetic trajectories and a deep learning model for user identification which safeguards privacy. These two modules are combined with a next-week trajectory predictor that uses privacy-aware synthetic data. The experiments on two real-life datasets show that the generator creates trajectories similar to the real ones yet different enough to safeguard privacy. The low user-recognition recognition accuracy of models trained on the generated data demonstrates privacy awareness. Statistical tests confirm no significant difference between the original and the generated trajectories. We further demonstrate the utility of the synthetic data by predicting week-ahead trajectories based on the synthetic trajectories. Our study shows how privacy and utility can be managed jointly using the proposed privacy-aware approach.

The diffusion identification in a SIS reaction-diffusion system.

This article is concerned with the determination of the diffusion matrix in the reaction-diffusion mathematical model arising from the spread of an epidemic. The mathematical model that we consider is a susceptible-infected-susceptible model with diffusion, which was deduced by assuming the following hypotheses: The total population can be partitioned into susceptible and infected individuals; a healthy susceptible individual becomes infected through contact with an infected individual; there is no immunity, and infected individuals can become susceptible again; the spread of epidemics arises in a spatially heterogeneous environment; the susceptible and infected individuals implement strategies to avoid each other by staying away. The spread of the dynamics is governed by an initial boundary value problem for a reaction-diffusion system, where the model unknowns are the densities of susceptible and infected individuals and the boundary condition models the fact that there is neither emigration nor immigration through their boundary. The reaction consists of two terms modeling disease transmission and infection recovery, and the diffusion is a space-dependent full diffusion matrix. The determination of the diffusion matrix was conducted by considering that we have experimental data on the infective and susceptible densities at some fixed time and in the overall domain where the population lives. We reformulated the identification problem as an optimal control problem where the cost function is a regularized least squares function. The fundamental contributions of this article are the following: The existence of at least one solution to the optimization problem or, equivalently, the diffusion identification problem; the introduction of first-order necessary optimality conditions; and the necessary conditions that imply a local uniqueness result of the inverse problem. In addition, we considered two numerical examples for the case of parameter identification.

Exploring human mixing patterns based on time use and social contact data and their implications for infectious disease transmission models

BackgroundThe increasing availability of data on social contact patterns and time use provides invaluable information for studying transmission dynamics of infectious diseases. Social contact data provide information on the interaction of people in a population whereas the value of time use data lies in the quantification of exposure patterns. Both have been used as proxies for transmission risks within in a population and the combination of both sources has led to investigate which contacts are more suitable to describe these transmission risks.MethodsWe used social contact and time use data from 1707 participants from a survey conducted in Flanders, Belgium in 2010–2011. We calculated weighted exposure time and social contact matrices to analyze age- and gender-specific mixing patterns and to quantify behavioral changes by distance from home. We compared the value of both separate and combined data sources for explaining seroprevalence and incidence data on parvovirus-B19, Varicella-Zoster virus (VZV) and influenza like illnesses (ILI), respectively.ResultsAssortative mixing and inter-generational interaction is more pronounced in the exposure matrix due to the high proportion of time spent at home. This pattern is less pronounced in the social contact matrix, which is more impacted by the reported contacts at school and work. The average number of contacts declined with distance. On the individual-level, we observed an increase in the number of contacts and the transmission potential by distance when travelling. We found that both social contact data and time use data provide a good match with the seroprevalence and incidence data at hand. When comparing the use of different combinations of both data sources, we found that the social contact matrix based on close contacts of at least 4 h appeared to be the best proxy for parvovirus-B19 transmission. Social contacts and exposure time were both on their own able to explain VZV seroprevalence data though combining both scored best. Compared with the contact approach, the time use approach provided the better fit to the ILI incidence data.ConclusionsOur work emphasises the common and complementary value of time use and social contact data for analysing mixing behavior and analysing infectious disease transmission. We derived spatial, temporal, age-, gender- and distance-specific mixing patterns, which are informative for future modelling studies.

Vaccination effect on the dynamics of dengue disease transmission models in Nepal: A fractional derivative approach

Dengue is a vector-borne disease which is spreading rapidly around the world. It is one of the fastly growing public health problems in Nepal. Since 2004, dengue cases have been recorded in both tropical and subtropical regions of Nepal. There is no specific treatment for the dengue disease, which is brought on by the dengue virus. This study attempts the use of the Caputo fractional-order derivative to suggest SVEIRP-SEI epidemic model that integrates vaccination and hospitalization in order to precisely analyze the transmission of dengue infection phenomena. The existence and uniqueness are discussed for the model solutions. Basic reproduction number R0 with vaccination is formulated using next generation matrix. Both the local and global stability of disease free and endemic equilibrium points are explored. The parameters are estimated from the actual outbreak of infected cases in Nepal. Sensitivity analysis is then presented graphically with appropriate memory index ψ. The findings of the mathematical and simulation results demonstrate that vaccination is one of the effective strategies that lowers the prevalence of the disease significantly.

Testing a simple and frugal model of health protective behaviour in epidemic times

The COVID-19 epidemic highlighted the necessity to integrate dynamic human behaviour change into infectious disease transmission models. The adoption of health protective behaviour, such as handwashing or staying at home, depends on both epidemiological and personal variables. However, only a few models have been proposed in the recent literature to account for behavioural change in response to the health threat over time. This study aims to estimate the relevance of TELL ME, a simple and frugal agent-based model developed following the 2009 H1N1 outbreak to explain individual engagement in health protective behaviours in epidemic times and how communication can influence this. Basically, TELL ME includes a behavioural rule to simulate individual decisions to adopt health protective behaviours. To test this rule, we used behavioural data from a series of 12 cross-sectional surveys in France over a 6-month period (May to November 2020). Samples were representative of the French population (N = 24,003). We found the TELL ME behavioural rule to be associated with a moderate to high error rate in representing the adoption of behaviours, indicating that parameter values are not constant over time and that other key variables influence individual decisions. These results highlight the crucial need for longitudinal behavioural data to better calibrate epidemiological models accounting for public responses to infectious disease threats.

Leveraging infectious disease models to interpret randomized controlled trials: Controlling enteric pathogen transmission through water, sanitation, and hygiene interventions.

Randomized controlled trials (RCTs) evaluate hypotheses in specific contexts and are often considered the gold standard of evidence for infectious disease interventions, but their results cannot immediately generalize to other contexts (e.g., different populations, interventions, or disease burdens). Mechanistic models are one approach to generalizing findings between contexts, but infectious disease transmission models (IDTMs) are not immediately suited for analyzing RCTs, since they often rely on time-series surveillance data. We developed an IDTM framework to explain relative risk outcomes of an infectious disease RCT and applied it to a water, sanitation, and hygiene (WASH) RCT. This model can generalize the RCT results to other contexts and conditions. We developed this compartmental IDTM framework to account for key WASH RCT factors: i) transmission across multiple environmental pathways, ii) multiple interventions applied individually and in combination, iii) adherence to interventions or preexisting conditions, and iv) the impact of individuals not enrolled in the study. We employed a hybrid sampling and estimation framework to obtain posterior estimates of mechanistic parameter sets consistent with empirical outcomes. We illustrated our model using WASH Benefits Bangladesh RCT data (n = 17,187). Our model reproduced reported diarrheal prevalence in this RCT. The baseline estimate of the basic reproduction number [Formula: see text] for the control arm (1.10, 95% CrI: 1.07, 1.16) corresponded to an endemic prevalence of 9.5% (95% CrI: 7.4, 13.7%) in the absence of interventions or preexisting WASH conditions. No single pathway was likely able to sustain transmission: pathway-specific [Formula: see text] for water, fomites, and all other pathways were 0.42 (95% CrI: 0.03, 0.97), 0.20 (95% CrI: 0.02, 0.59), and 0.48 (95% CrI: 0.02, 0.94), respectively. An IDTM approach to evaluating RCTs can complement RCT analysis by providing a rigorous framework for generating data-driven hypotheses that explain trial findings, particularly unexpected null results, opening up existing data to deeper epidemiological understanding.

A mathematical prediction model of infectious diseases considering vaccine and temperature, and its prediction in Hong Kong

Since 2020, COVID-19 has launched a rather difficult challenge in public health all over the world. For the current situation of COVID-19 outbreaks in various places, predicting the trend of COVID-19 plays a vital role in later policy-making, allocating medical materials, and developing the economy and society. Although there may be corresponding specific drugs soon, which can reduce the mortality of COVID-19 to a relatively low level, but the main popular Omicron BA.1 and BA.2 strain is highly infectious, which has a great impact on the elderly population, so COVID-19 cannot be equated with general influenza. This paper aims to predict the trend of the number of infections over time and the final number of infections from the fifth wave of epidemic in Hong Kong. To establish a more practical infection model, this paper introduces an infectious disease transmission model with the influence of temperature and vaccine. The model shows that the fifth wave of the epidemic in Hong Kong will end at the end of April 2022. At that time, the cumulative number of infections is expected to reach about 1.6 million. By formulating and implementing reasonable policies, the final number of infections can be controlled at about 1.1 million. Therefore, we hope that the policymakers and managers of COVID-19 in Hong Kong will formulate and adopt reasonable measures to control these epidemic.

Return on Investment of the COVID-19 Vaccination Campaign in New York City

New York City, an early epicenter of the pandemic, invested heavily in its COVID-19 vaccination campaign to mitigate the burden of disease outbreaks. Understanding the return on investment (ROI) of this campaign would provide insights into vaccination programs to curb future COVID-19 outbreaks. To estimate the ROI of the New York City COVID-19 vaccination campaign by estimating the tangible direct and indirect costs from a societal perspective. This decision analytical model of disease transmission was calibrated to confirmed and probable cases of COVID-19 in New York City between December 14, 2020, and January 31, 2022. This simulation model was validated with observed patterns of reported hospitalizations and deaths during the same period. An agent-based counterfactual scenario without vaccination was simulated using the calibrated model. Costs of health care and deaths were estimated in the actual pandemic trajectory with vaccination and in the counterfactual scenario without vaccination. The savings achieved by vaccination, which were associated with fewer outpatient visits, emergency department visits, emergency medical services, hospitalizations, and intensive care unit admissions, were also estimated. The value of a statistical life (VSL) lost due to COVID-19 death and the productivity loss from illness were accounted for in calculating the ROI. During the study period, the vaccination campaign averted an estimated $27.96 (95% credible interval [CrI], $26.19-$29.84) billion in health care expenditures and 315 724 (95% CrI, 292 143-340 420) potential years of life lost, averting VSL loss of $26.27 (95% CrI, $24.39-$28.21) billion. The estimated net savings attributable to vaccination were $51.77 (95% CrI, $48.50-$55.85) billion. Every $1 invested in vaccination yielded estimated savings of $10.19 (95% CrI, $9.39-$10.87) in direct and indirect costs of health outcomes that would have been incurred without vaccination. Results of this modeling study showed an association of the New York City COVID-19 vaccination campaign with reduction in severe outcomes and avoidance of substantial economic losses. This significant ROI supports continued investment in improving vaccine uptake during the ongoing pandemic.

Incorporating human dynamic populations in models of infectious disease transmission: a systematic review

BackgroundAn increasing number of infectious disease models consider demographic change in the host population, but the demographic methods and assumptions vary considerably. We carry out a systematic review of the methods and assumptions used to incorporate dynamic populations in infectious disease models.MethodsWe systematically searched PubMed and Web of Science for articles on infectious disease transmission in dynamic host populations. We screened the articles and extracted data in accordance with the guidelines of the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA).ResultsWe identified 46 articles containing 53 infectious disease models with dynamic populations. Population dynamics were modelled explicitly in 71% of the disease transmission models using cohort-component-based models (CCBMs) or individual-based models (IBMs), while 29% used population prospects as an external input. Fertility and mortality were in most cases age- or age-sex-specific, but several models used crude fertility rates (40%). Households were incorporated in 15% of the models, which were IBMs except for one model using external population prospects. Finally, 17% of the infectious disease models included demographic sensitivity analyses.ConclusionsWe find that most studies model fertility, mortality and migration explicitly. Moreover, population-level modelling was more common than IBMs. Demographic characteristics beyond age and sex are cumbersome to implement in population-level models and were for that reason only incorporated in IBMs. Several IBMs included households and networks, but the granularity of the underlying demographic processes was often similar to that of CCBMs. We describe the implications of the most common assumptions and discuss possible extensions.

Dynamic model of respiratory infectious disease transmission by population mobility based on city network.

In modern societies, newly emerging infectious diseases spread rapidly between regions owing to frequent contact between people, causing considerable social and economic impacts. In this study, first, a scale-free city network was established, and then the shortest path between any two nodes was determined. Second, the movement path of tourists was designed based on the shortest path. Subsequently, every infected person's information, such as the city, infection time, onset and hospitalization, was confirmed based on their movement path. Third, the features of the transmission path and time distribution of the epidemic were characterized after summarizing the information. Finally, the reliability of the model was verified. The number of citizens and tourists in every city remained stable during this time. The results indicated that a larger basic reproduction number (R 0) and population outflow rate signify a faster growth rate of infected people in each city in the network. Compared with small and medium-sized cities, the epidemic spread faster in central cities. Population mobility was the decisive factor causing the spread of the epidemic to other areas. Therefore, the rapid spread of epidemics can be prevented by swiftly reducing the flow of people between cities.