Disease Transmission Model Research Articles

DETERMINISTIC AND STOCHASTIC MODEL FOR THE TRANSMISSION OF LASSA FEVER

Many models on the transmission dynamics of Lasser fever were based on purely deterministic approach. This approach does not put into cognizance randomness which is inherent in disease transmission resulting from differences in immunity levels, contact patterns, hygienic practices and mutation rates among so many other possibilities. In this work, we attempt to demonstrate the impact of uncertainties in the mode of transmission of Lassa fever by subjecting the dynamics to some white noise modeled by the Brownian motion as a Wiener process. An existing deterministic model involving the Susceptible, Exposed, Infected and Recovered (SEIR) individuals was transformed into a stochastic differential equation model by applying the procedure proposed by Allen et al (2008). The resulting system of Stochastic Differential Equations (SDE) was solved numerically using the Milstein scheme for SDEs. An algorithm for the method was developed and implemented in Python programming language. Numerical simulations of the model was done using four sets of parameters; , representing the natural birth rate, the natural death rate , the recovering rate from infected to recovered, transmission rate from exposed to infected ,transmission rate from susceptible to exposed are carried out to investigate the transmission dynamic of Lassa fever. The results of the simulations indicate that randomness does affect transmission of Lassa fever. We therefore recommend that factors such as social behavior, hygienic practices, contact patters, mutation rate should be considered while formulating mathematics models of disease transmission.

Model-based impact evaluation of new tuberculosis vaccines in aging populations under different modeling scenarios: the case of China.

The slow descent in TB burden, the COVID-19 pandemic, along with the rise of multidrug-resistant strains of Mycobacterium tuberculosis, seriously threaten TB control and the goals of the End TB strategy. To fight back, several vaccine candidates are under development, with some of them undergoing the phases 2B and 3 of the development pipeline. The impact of these vaccines on the general population needs to be addressed using disease-transmission models, and, in a country like China, which last year ranked third in number of cases worldwide, and where the population is aging at a fast pace, the impact of TB vaccination campaigns may depend heavily upon the age of targeted populations, the mechanistic descriptions of the TB vaccines and the coupling between TB dynamics and demographic evolution. In this work, we studied the potential impact of a new TB vaccine in China targeting adolescents (15-19 y.o.) or older adults (60-64 y.o.), according to varying vaccine descriptions that represent reasonable mechanisms of action leading to prevention of disease, or prevention of recurrence, each of them targetting specific routes to TB disease. To measure the influence of the description of the coupling between transmission dynamics and aging in TB transmission models, we explored two different approaches to compute the evolution of the contact matrices, which relate to the spreading among different age strata. Our findings highlight the dependence of model-based impact estimates on vaccine profiles and the chosen modeling approach for describing the evolution of contact matrices. Our results also show, in line with previous modeling works, that older adult vaccination is a suitable option in China to reduce the incidence of TB as long as the vaccine is able to protect already exposed individuals. This study underscores the importance of considering vaccine characteristics and demographic dynamics in shaping TB control strategies. In this sense, older adult vaccination emerges as a promising avenue for mitigating TB transmission in China but also remarks the need for tailored intervention strategies aligned with demographic trends.

Modelling disease transmission through asymptomatic carriers: a societal and environmental perspective

Modelling disease transmission through asymptomatic carriers: a societal and environmental perspective

Unexpected behavioural adaptation of yellow fever mosquitoes in response to high temperatures

Temperature is a major ecological driver of mosquito-borne diseases as it influences the life-history of both the mosquito and the pathogen harboured within it. Understanding the mosquitoes’ thermal biology is essential to inform risk prediction models of such diseases. Mosquitoes can respond to temperatures by microhabitat selection through thermal preference. However, it has not yet been considered that mosquitoes are likely to adapt to changing temperatures, for example during climate change, and alter their preference over evolutionary time. We investigated this by rearing six cohorts of the yellow fever mosquito Aedes aegypti at two temperatures (24 °C, 30 °C) for 20 generations and used these cohorts to explicitly separate the effects of long-term evolution and within-generation acclimation on their thermal preferences in a thermal gradient of 20–35 °C. We found that warm-evolved mosquitoes spent 31.5% less time at high temperatures, which affects their efficiency as a vector. This study reveals the complex interplay of experimental evolution, rearing temperatures, and thermal preference in Ae. aegypti mosquitoes. It highlights the significance of incorporating mosquito microhabitat selection in disease transmission models, especially in the context of climate change.

A beta-Poisson model for infectious disease transmission.

Outbreaks of emerging and zoonotic infections represent a substantial threat to human health and well-being. These outbreaks tend to be characterised by highly stochastic transmission dynamics with intense variation in transmission potential between cases. The negative binomial distribution is commonly used as a model for transmission in the early stages of an epidemic as it has a natural interpretation as the convolution of a Poisson contact process and a gamma-distributed infectivity. In this study we expand upon the negative binomial model by introducing a beta-Poisson mixture model in which infectious individuals make contacts at the points of a Poisson process and then transmit infection along these contacts with a beta-distributed probability. We show that the negative binomial distribution is a limit case of this model, as is the zero-inflated Poisson distribution obtained by combining a Poisson-distributed contact process with an additional failure probability. We assess the beta-Poisson model's applicability by fitting it to secondary case distributions (the distribution of the number of subsequent cases generated by a single case) estimated from outbreaks covering a range of pathogens and geographical settings. We find that while the beta-Poisson mixture can achieve a closer to fit to data than the negative binomial distribution, it is consistently outperformed by the negative binomial in terms of Akaike Information Criterion, making it a suboptimal choice on parsimonious grounds. The beta-Poisson performs similarly to the negative binomial model in its ability to capture features of the secondary case distribution such as overdispersion, prevalence of superspreaders, and the probability of a case generating zero subsequent cases. Despite this possible shortcoming, the beta-Poisson distribution may still be of interest in the context of intervention modelling since its structure allows for the simulation of measures which change contact structures while leaving individual-level infectivity unchanged, and vice-versa.

Leptospirosis Relative Risk Estimates based on Continuous-Time, Discrete-Space Stochastic SIR-L-SI Transmission Model

Leptospirosis is a re-emerging global disease that has become endemic in Malaysia. The transmissions usually occur between animals especially rats to rats and rats to humans. Since, it is an easily contractable disease that can be transmitted directly through contact with infected rat’s urine or indirectly from the environment such as via water and soil, it is very challenging to curb this disease from infecting humans. Poor understanding of the disease and lack of epidemiological data also made leptospirosis is difficult to control. To cope with this problem, a leptospirosis disease transmission model is developed to study the mechanism of leptospirosis disease spread over continuous-time that may help to predict future caused of an outbreak. This study aims to construct a continuous-time and discrete-space stochastic SIR-L-SI (Susceptible, Infected, Recovered Humans-Leptospires in the Environment-Susceptible, Infectious Rats) of leptospirosis disease transmission to estimate the risk involved. A simple method of asymptotic and numerical analyses is applied as an alternative approach for solving simultaneous differential equations in the leptospirosis SIR-L-SI transmission model. The application of the proposed model is demonstrated using leptospirosis data for Malaysia. The results of asymptotic behaviour and numerical analysis provide useful information about susceptible and infective rat and human populations as well as offer relative risk estimates that can be used as one of the control measures in identifying hot-spot areas for this disease.

Contributing to health system resilience during pandemics via purchasing and supply strategies: an exploratory system dynamics approach

BackgroundHealth systems worldwide struggled to obtain sufficient personal protective equipment (PPE) and ventilators during the COVID-19 pandemic due to global supply chain disruptions. Our study’s aim was to create a proof-of-concept model that would simulate the effects of supply strategies under various scenarios, to ultimately help decision-makers decide on alternative supply strategies for future similar health system related crises.MethodsWe developed a system dynamics model that linked a disease transmission model structure (susceptible, exposed, infectious, recovered (SEIR)) with a model for the availability of critical supplies in hospitals; thereby connecting care demand (patients’ critical care in hospitals), with care supply (available critical equipment and supplies). To inform the model structure, we used data on critical decisions and events taking place surrounding purchase, supply, and availability of PPE and ventilators during the first phase of the COVID-19 pandemic within the English national health system. We used exploratory modelling and analysis to assess the effects of uncertainties on different supply strategies in the English health system under different scenarios. Strategies analysed were: (i) purchasing from the world market or (ii) through direct tender, (iii) stockpiling, (iv) domestic production, (v) supporting innovative supply strategies, or (vi) loaning ventilators from the private sector.ResultsWe found through our exploratory analysis that a long-lasting shortage in PPE and ventilators is likely to be apparent in various scenarios. When considering the worst-case scenario, our proof-of-concept model shows that purchasing PPE and ventilators from the world market or through direct tender have the greatest influence on reducing supply shortages, compared to producing domestically or through supporting innovative supply strategies. However, these supply strategies are affected most by delays in their shipment time or set-up.ConclusionWe demonstrated that using a system dynamics and exploratory modelling approach can be helpful in identifying the purchasing and supply chain strategies that contribute to the preparedness and responsiveness of health systems during crises. Our results suggest that to improve health systems’ resilience during pandemics or similar resource-constrained situations, purchasing and supply chain decision-makers can develop crisis frameworks that propose a plan of action and consequently accelerate and improve procurement processes and other governance processes during health-related crises; implement diverse supplier frameworks; and (re)consider stockpiling. This proof-of-concept model demonstrates the importance of including critical supply chain strategies as part of the preparedness and response activities to contribute to health system resilience.

Numerical analysis of the SIS infectious disease model with spatial heterogeneity

PurposeThe susceptible-infectious-susceptible (SIS) infectious disease models without spatial heterogeneity have limited applications, and the numerical simulation without considering models’ global existence and uniqueness of classical solutions might converge to an impractical solution. This paper aims to develop a robust and reliable numerical approach to the SIS epidemic model with spatial heterogeneity, which characterizes the horizontal and vertical transmission of the disease.Design/methodology/approachThis study used stability analysis methods from nonlinear dynamics to evaluate the stability of SIS epidemic models. Additionally, the authors applied numerical solution methods from diffusion equations and heat conduction equations in fluid mechanics to infectious disease transmission models with spatial heterogeneity, which can guarantee a robustly stable and highly reliable numerical process. The findings revealed that this interdisciplinary approach not only provides a more comprehensive understanding of the propagation patterns of infectious diseases across various spatial environments but also offers new application directions in the fields of fluid mechanics and heat flow. The results of this study are highly significant for developing effective control strategies against infectious diseases while offering new ideas and methods for related fields of research.FindingsThrough theoretical analysis and numerical simulation, the distribution of infected persons in heterogeneous environments is closely related to the location parameters. The finding is suitable for clinical use.Originality/valueThe theoretical analysis of the stability theorem and the threshold dynamics guarantee robust stability and fast convergence of the numerical solution. It opens up a new window for a robust and reliable numerical study.

Near-term forecasting of Covid-19 cases and hospitalisations in Aotearoa New Zealand.

Near-term forecasting of infectious disease incidence and consequent demand for acute healthcare services can support capacity planning and public health responses. Despite well-developed scenario modelling to support the Covid-19 response, Aotearoa New Zealand lacks advanced infectious disease forecasting capacity. We develop a model using Aotearoa New Zealand's unique Covid-19 data streams to predict reported Covid-19 cases, hospital admissions and hospital occupancy. The method combines a semi-mechanistic model for disease transmission to predict cases with Gaussian process regression models to predict the fraction of reported cases that will require hospital treatment. We evaluate forecast performance against out-of-sample data over the period from 2 October 2022 to 23 July 2023. Our results show that forecast performance is reasonably good over a 1-3 week time horizon, although generally deteriorates as the time horizon is lengthened. The model has been operationalised to provide weekly national and regional forecasts in real-time. This study is an important step towards development of more sophisticated situational awareness and infectious disease forecasting tools in Aotearoa New Zealand.

Wildlife vaccination strategies for eliminating bovine tuberculosis in white-tailed deer populations.

Many pathogens of humans and livestock also infect wildlife that can act as a reservoir and challenge disease control or elimination. Efficient and effective prioritization of research and management actions requires an understanding of the potential for new tools to improve elimination probability with feasible deployment strategies that can be implemented at scale. Wildlife vaccination is gaining interest as a tool for managing several wildlife diseases. To evaluate the effect of vaccinating white-tailed deer (Odocoileus virginianus), in combination with harvest, in reducing and eliminating bovine tuberculosis from deer populations in Michigan, we developed a mechanistic age-structured disease transmission model for bovine tuberculosis with integrated disease management. We evaluated the impact of pulse vaccination across a range of vaccine properties. Pulse vaccination was effective for reducing disease prevalence rapidly with even low (30%) to moderate (60%) vaccine coverage of the susceptible and exposed deer population and was further improved when combined with increased harvest. The impact of increased harvest depended on the relative strength of transmission modes, i.e., direct vs indirect transmission. Vaccine coverage and efficacy were the most important vaccine properties for reducing and eliminating disease from the local population. By fitting the model to the core endemic area of bovine tuberculosis in Michigan, USA, we identified feasible integrated management strategies involving vaccination and increased harvest that reduced disease prevalence in free-ranging deer. Few scenarios led to disease elimination due to the chronic nature of bovine tuberculosis. A long-term commitment to regular vaccination campaigns, and further research on increasing vaccines efficacy and uptake rate in free-ranging deer are important for disease management.

Dynamics in a delayed rumor propagation model with logistic growth and saturation incidence

<abstract><p>This paper studies a delayed rumor propagation model with logistic growth and saturation incidence. The next generation matrix method, some inequality techniques, the Lyapunov-LaSalle invariance principle, and the Lyapunov method are used in this paper. Our results indicate that if the basic regeneration number (which is analogous to the basic reproduction number in disease transmission models) is less than 1, the rumor-free equilibrium point (which is analogous to the disease-free equilibrium point in disease transmission models) is globally stable. If the basic regeneration number is greater than 1, then the rumor is permanent, and some sufficient conditions are obtained for local and global asymptotic stability of the rumor prevailing equilibrium point (which is analogous to the endemic equilibrium point in disease transmission models). Finally, three examples with numerical simulations are presented to illustrate the obtained theoretical results.</p></abstract>

Simulation of Premovement Active Surveillance Protocols for Moving Finishing Pigs to a Harvest Facility from a Control Area during an Outbreak of African Swine Fever in the United States

Movement restrictions are a critical component of response plans for an African swine fever (ASF) outbreak in the United States. These restrictions are likely to include requiring permits to move animals and products within, into, and out of 5‐km control areas (CAs) established around confirmed positive farms. For quarantined finishing farms located within a CA, diagnostic testing is an expected criterion for receival of a permit to move pigs to a harvest facility or removal of quarantine. A stochastic disease transmission and active surveillance model were used to evaluate premovement active surveillance protocols varying by the number of samples and timing of sample collection before movement. Surveillance protocol scenarios were evaluated for several different sampling prioritization schemes; virus strains of medium or high virulence; barn sizes of 1,200, 2,400, and 4,800 pigs; and farms with average to high mortality and morbidity during routine production. Surveillance protocols that included prioritization schemes targeting dead pigs and pigs with clinical signs resulted in the highest probabilities of detection and the lowest numbers of infectious pigs at the time of movement in barns that went undetected. There was some evidence that targeting sick pigs prior to dead pigs may be more effective for moderately virulent strains. However, in most scenarios, including all highly virulent strain scenarios and moderately virulent strain scenarios in barn sizes of 1,200 with average farm performance, prioritization of dead versus sick pigs first did not have a large impact on the predicted outcomes. Increasing sample sizes improved outcomes, though only marginal gains were achieved once the available dead and sick were sampled. Predicted outcomes may be further improved by sampling the available dead and sick pigs in a barn across multiple days, though the associated increase in the probability of detection was minor.

The effect of insecticide in tungro disease transmission model with vegetative and generative phase

The effect of insecticide in tungro disease transmission model with vegetative and generative phase

A competitive infectious transmission model

Compartmental disease transmission models are widely used to model state transmission in infectious diseases, using differential equations to model the change in the number of units in different states over time, and recently has produced significant practical implications in many downstream fields. However, inspired by the transmission of rumors in social media, we note that the previous compartmental transfer models neglect the "competitiveness" during the transfer process, that is, the "infection" of people with positive and negative opinions to "susceptibles" or even people with opposing views. To tackle the above issues, in this paper, we propose a novel competitive infectious transmission model in which the "infection" will lead to more people supporting the opinion of the infector, effectively establishing the change of the number of units in the positive, negative, and neutral parties over time. In addition, we performed extensive theoretical analysis to investigate the property of the disease-free equilibrium and to calculate the basic reproduction numbers for three different scenarios. For each system, we derive explicit solutions for the basic reproduction numbers and discuss their important implications for guidance in practice.

EE597 Data on Human Population Mobility in Individual-Based Models of Infectious Disease Transmission: A Systematic Review

EE597 Data on Human Population Mobility in Individual-Based Models of Infectious Disease Transmission: A Systematic Review

PP118 The Value Of New Antibiotic Treatment Strategies In Zhejiang Province, China

IntroductionThe rising antimicrobial resistance (AMR) and the difficulty in developing new antibiotics are causing a global public health problem. This analysis aims to better understand the clinical and economic value of new antibiotic treatment strategies, in order to inform clinical and antibiotic formulary decisions.MethodsWe applied a published and validated dynamic disease transmission and cost-effectiveness model of AMR with a 10-year time horizon and discount rate of five percent to evaluate the clinical and economic outcomes of introducing a new antibiotic, namely, Ceftazidime/Avibactam (CAZ-AVI) for treating AMR infections in Zhejiang Province, China. Together with piperacillin-tazobactam (pip/taz) and meropenem, we explored the impact of six treatment strategies across three common infections (complicated intra-abdominal infection (cIAI), hospital-acquired/ventilator-associated pneumonia (HAP/VAP) and infections with limited treatment options (LTO)), and pathogens (Escherichia coli, Klebsiella spp., and Pseudomonas aeruginosa). These treatment strategies included (i) current treatment strategy (pip/taz and meropenem, no CAZ-AVI), (ii) CAZ-AVI at the third line, (iii) CAZ-AVI at the second line, (iv) CAZ-AVI at the first line, (v) first line diversity (i.e., equal pip/taz and CAZ-AVI at the first line; meropenem at the last line) and (vi) all-lines diversity (pip/taz, meropenem and CAZ-AVI used randomly and only once). The data with a total of 10,905 patients were collected from a tier-3 hospital from 2018 to 2021.ResultsUnder the current treatment strategy, the hospital length of stay (LOS) and costs over ten years were estimated to be 1,588,763 days and CNY3,898,198,802 (USD559,781,348), respectively, associated with 142,999 quality-adjusted life-years (QALYs) lost, resulting in the resistance of pip/taz and meropenem being 42.0 percent and 49.9 percent respectively. In contrast, the other five treatment strategies all have shown improved outcomes, among which the “all-lines diversity” carried the greatest benefit, saving CNY1,646.04 (USD236.37) for each additional QALY gained, with the net monetary benefit being CNY24,727,102,215 (USD3,550,811,878).ConclusionsIntroducing CAZ-AVI had positive impact on clinical and economic outcomes for treating AMR, and diversifying early the antibiotics might yield the best benefits.

ANALISIS KESTABILAN MODEL SI UNTUK PENYAKIT MENULAR DENGAN ADANYA TRANSMISI VERTIKAL DAN TINGKAT KEJADIAN JENUH

The transmission of infectious diseases can occur through two pathways: horizontal and vertical. Horizontal transmission occurs through direct or indirect physical contact with the infectious agent, while vertical transmission takes place when an infected mother transmits the disease to a fetus or a newborn. Within the context of disease transmission models, a critical feature is the saturation incidence rate, which refers to the impact of interventions that can reduce the rate of disease transmission among susceptible and infected individuals. This research aims to elucidate the formation of a model, determine equilibrium points, and calculate the basic reproduction number using the Next Generation Matrix method. The analysis involves assessing local stability through linearization methods and global stability using Lyapunov functions. Sensitivity analysis is conducted on the basic reproduction number, and numerical simulations are performed using the fourth-order Runge-Kutta method. The research findings indicate the establishment of an SIS (Susceptible-Infected) model for infectious diseases with vertical transmission and saturation incidence. This model depicts the spread of the disease in a population, where individuals can exist in susceptible or infected conditions. Equilibrium points include a disease-free equilibrium that is locally and globally stable when the basic reproduction number is less than one, and an endemic equilibrium that is locally and globally stable when the basic reproduction number exceeds one. Sensitivity analysis reveals that each parameter has varying influences on the basic reproduction number. An increase in the saturation incidence rate leads to a decrease in the number of infected subpopulations, while an increase in the vertical transmission rate results in a similar decline. Numerical simulations support stability analyses at equilibrium points. These findings provide a deeper understanding of the factors influencing the spread of diseases within a population.

Variable screening methods in spatial infectious disease transmission models

Data-driven mathematical modelling can enrich our understanding of infectious disease spread enormously. Individual-level models of infectious disease transmission allow the incorporation of different individual-level covariates, such as spatial location, vaccination status, etc. This study aims to explore and develop methods for fitting such models when we have many potential covariates to include in the model. The aim is to enhance the performance and interpretability of models and ease the computational burden of fitting these models to data. We have applied and compared multiple variable selection methods in the context of spatial epidemic data. These include a Bayesian two-stage least absolute shrinkage and selection operator (Lasso), forward and backward stepwise selection based on the Akaike information criterion (AIC), spike-and-slab priors, and random variable selection (boosting) methods. We discuss and compare the performance of these methods via simulated datasets and UK 2001 foot-and-mouth disease data. While comparing the variable selection methods all performed consistently well except the two-stage Lasso. We conclude that the spike-and-slab prior method is to be recommended, consistently resulting in high accuracy and short computational time.

The spatiotemporal analysis of the population migration network in China, 2021

Population migration is a critical component of large-scale spatiotemporal models of infectious disease transmission. Identifying the most influential spreaders in networks is vital to controlling and understanding the spreading process of infectious diseases. We used Baidu Migration data for the whole year of 2021 to build mobility networks. The nodes of the network represent cities, and the edges represent the population flow between cities. By applying the k-shell decomposition and the Louvain algorithm, we could get the k-shell values for each city and community partition. Then, we identified the most efficient nodes or pathways in a complex network by generating random networks. Furthermore, we analyzed the eigenvalue of the migration matrix to find the nodes that have the most impact on the network. We also found the consistency between k-shell value and eigenvalue through Kendall's τ test. The main result is that in Spring Festival and National Day, the network is at higher risk of an infectious disease outbreak and the Yangtze River Delta is at the highest risk of an epidemic all year around. Shanghai is the most significant node in both k-shell value and eigenvalue analysis. The spatiotemporal property of the network should be taken into account to model the transmission of infectious diseases more accurately.

Incorporating heterogeneity in farmer disease control behaviour into a livestock disease transmission model.

Human behaviour is critical to effective responses to livestock disease outbreaks, especially with respect to vaccination uptake. Traditionally, mathematical models used to inform this behaviour have not taken heterogeneity in farmer behaviour into account. We address this by exploring how heterogeneity in farmers vaccination behaviour can be incorporated to inform mathematical models. We developed and used a graphical user interface to elicit farmers (n=60) vaccination decisions to an unfolding fast-spreading epidemic and linked this to their psychosocial and behavioural profiles. We identified, via cluster analysis, robust patterns of heterogeneity in vaccination behaviour. By incorporating these vaccination behavioural groupings into a mathematical model for a fast-spreading livestock infection, using computational simulation we explored how the inclusion of heterogeneity in farmer disease control behaviour may impact epidemiological and economic focused outcomes. When assuming homogeneity in farmer behaviour versus configurations informed by the psychosocial profile cluster estimates, the modelled scenarios revealed a disconnect in projected distributions and threshold statistics across outbreak size, outbreak duration and economic metrics.