Search Results (24)

A compartmental, deterministic model was used to explore the effects of temperature dependency in mosquito mortality on the likelihood of epidemics and the size of outbreaks of Chikungunya virus under Florida temperature conditions. Two known vectors, Aedes albopictus and Ae. aegypti, were included, with similar structure but allowing mortality and abundance parameters to vary between them. The mortality relationship with temperature had a central optimal survival region, with increasing mortality outside these regions. The central temperature and the annual mean temperature were most influential in the likelihood of an epidemic, although the variance explained was low. The central temperature, annual mean temperature and day of virus infection influenced the size of the outbreaks. Regression models including two-way interactions explained more of the variance in outcomes than the main effects models, but there was still substantial variance left unexplained. Given the model structure, higher order interactions would be required to explain most of the variance. Full article

Mass-balanced compartmental systems defy classical deterministic entropy measures since both metric and topological entropy vanish in dissipative dynamics. By interpreting open compartmental systems as absorbing continuous-time Markov chains that describe the random journey of a single representative particle, we allow established information-theoretic principles to be applied to this particular type of deterministic dynamical system. In particular, path entropy quantifies the uncertainty of complete trajectories, while entropy rates measure the average uncertainty of instantaneous transitions. Using Shannon’s information entropy, we derive closed-form expressions for these quantities in equilibrium and extend the maximum entropy principle (MaxEnt) to the problem of model selection in compartmental dynamics. This information-theoretic framework not only provides a systematic way to address equifinality but also reveals hidden structural properties of complex systems such as the global carbon cycle. Full article

Background: Tuberculosis (TB) remains a major global health challenge, including in Thailand, where both asymptomatic and symptomatic cases sustain transmission. The disease burden increases treatment complexity and mortality, requiring integrated care and coordinated policies. Methods: We developed a deterministic compartmental model to examine the transmission dynamics of TB in Thailand, incorporating both latent and active stages of infection, as well as vaccination coverage. The model was calibrated using national TB incidence data, and sensitivity analysis revealed that the TB transmission rate was the most influential parameter affecting the basic reproduction number (R₀). We evaluated the impact of several intervention strategies, including increased treatment coverage for latent and active TB infections and improved vaccination rates. Results: Our analysis indicates that among the single interventions, scaling up effective treatment for latent TB infections produced the greatest reduction in asymptomatic and symptomatic cases, while enhanced treatment for active TB cases was second most effective for reducing both asymptomatic and symptomatic cases. Importantly, our results indicate that combining multiple interventions yields significantly greater reductions in overall TB incidence than any single approach alone. Our findings suggest that a modest investment in integrated TB control can substantially reduce TB transmission and disease burden in Thailand. However, complete eradication of TB would require a comprehensive and sustained investment to achieve near-universal coverage of both preventive and curative strategies. Conclusions: TB remains a significant public health threat in Thailand. Targeted interventions and integrated strategies are key to reducing disease burden and improving treatment outcomes. Full article

This study presents a comprehensive analysis of zoonotic disease transmission dynamics between baboon and human populations using both deterministic and stochastic modeling approaches. The model is constructed with a symmetric compartmental structure for each species—susceptible, infected, and recovered—which reflects a biological and mathematical symmetry between the two interacting populations. Public health control strategies such as sterilization, restricted food access, and reduced human–baboon interaction are incorporated symmetrically, allowing for a balanced evaluation of their effectiveness across species. The basic reproduction number (${\mathcal{R}}_0$) is derived analytically and examined through sensitivity indices to identify critical epidemiological parameters. Numerical simulations, implemented via the Euler–Maruyama method, explore the influence of stochastic perturbations on disease trajectories. Statistical tools including Maximum Likelihood Estimation (MLE), Mean Squared Error (MSE), and Power Spectral Density (PSD) analysis validate model predictions and assess variability across noise levels. The results provide probabilistic confidence intervals and highlight the robustness of the proposed control strategies. This symmetry-aware, dual-framework modeling approach offers novel insights into zoonotic disease management, particularly in ecologically dynamic regions with frequent human–wildlife interactions. Full article

Background: Understanding the dynamics of HIV transmission in heterogeneous populations is crucial for effective prevention strategies. This study introduces the Risk Modulation Point (RMP), a novel threshold identifying where HIV transmission transitions from unsustainable spread to self-sustaining epidemic dynamics. Methods: Using a deterministic, risk-stratified compartmental model, we examined HIV transmission across populations stratified into 100–200 risk groups, each characterized by behavioral heterogeneity modeled through a power-law distribution. The model captures key features of HIV progression, with simulations conducted across high- (~20%), moderate- (~5%), and low (~0.2%)-prevalence regimes. Results: Our findings reveal universal patterns in HIV dynamics. The RMP marks a consistent threshold across scenarios, separating low-risk groups where transmission is minimal from higher-risk groups sustaining the epidemic. Logistic growth in HIV prevalence across risk groups, with sharp transitions near the RMP, was observed universally. The force of infection follows power-law scaling, directly reflecting the level and nature of risk behavior within each group. Importantly, the location of the RMP remains largely invariant to the underlying sexual risk distribution, population resolution, and mixing patterns, making it applicable across both generalized and concentrated epidemics. Conclusion: The RMP framework offers actionable public health insights. It identifies key populations and transition regions for targeted interventions such as antiretroviral therapy and pre-exposure prophylaxis. By tracking shifts in the RMP, it also serves as an early warning indicator for epidemic transitions, guiding resource allocation and monitoring. The focus of the model on intrinsic epidemic dynamics, excluding external interventions, highlights its utility in uncovering fundamental transmission patterns. This study bridges theoretical modeling and practical application, providing a flexible framework for understanding HIV and other stratified epidemics. The findings advance HIV modeling by revealing generic patterns that transcend specific contexts, supporting data-driven public health strategies. Full article

Obtaining accurate forecasts for the evolution of epidemic outbreaks from deterministic compartmental models represents a major theoretical challenge. Recently, it has been shown that these models typically exhibit trajectory degeneracy, as different sets of epidemiological parameters yield comparable predictions at early stages of the outbreak but disparate future epidemic scenarios. In this study, we use the Doi–Peliti approach and extend the classical deterministic compartmental models to a quantum-like formalism to explore whether the uncertainty of epidemic forecasts is also shaped by the stochastic nature of epidemic processes. This approach allows us to obtain a probabilistic ensemble of trajectories, revealing that epidemic uncertainty is not uniform across time, being maximal around the epidemic peak and vanishing at both early and very late stages of the outbreak. Therefore, our results show that, independently of the models’ complexity, the stochasticity of contagion and recovery processes poses a natural constraint for the uncertainty of epidemic forecasts. Full article

Background & Aims: Hepatocellular carcinoma (HCC) presents a significant global health challenge, particularly among individuals with liver cirrhosis, with hepatitis C (HCV) a major cause. In people with HCV-related cirrhosis, an increased risk of HCC remains after cure. HCC surveillance with six monthly ultrasounds has been shown to improve survival. However, adherence to biannual screening is currently suboptimal. This study aimed to evaluate the effect of increased HCC surveillance uptake and improved ultrasound sensitivity on mortality among people with HCV-related cirrhosis post HCV cure. Methods: This study utilized mathematical modelling to assess HCC progression, surveillance, diagnosis, and treatment among individuals with cirrhosis who had successfully been treated for HCV. The deterministic compartmental model incorporated Barcelona Clinic Liver Cancer (BCLC) stages to simulate disease progression and diagnosis probabilities in 100 people with cirrhosis who had successfully been treated for hepatitis C over 10 years. Four interventions were modelled to assess their potential for improving life expectancy: realistic improvements to surveillance adherence, optimistic improvements to surveillance adherence, diagnosis sensitivity enhancements, and improved treatment efficacy Results: Realistic adherence improvements resulted in 9.8 (95% CI 7.9, 11.6) life years gained per cohort of 100 over a 10-year intervention period; 17.2 (13.9, 20.3) life years were achieved in optimistic adherence improvements. Diagnosis sensitivity improvements led to a 7.0 (3.6, 13.8) year gain in life years, and treatment improvements improved life years by 9.0 (7.5, 10.3) years. Conclusions: Regular HCC ultrasound surveillance remains crucial to reduce mortality among people with cured hepatitis C and cirrhosis. Our study highlights that even minor enhancements to adherence to ultrasound surveillance can significantly boost life expectancy across populations more effectively than strategies that increase surveillance sensitivity or treatment efficacy. Full article

The number of confirmed positive tests of various sexually transmitted infections has grown recently in the United Kingdom. The objective of this study is to propose a deterministic compartmental model to investigate gonorrhoea spread in Northern Ireland between 2012 and 2022. The differential equation based model includes both symptomatic and asymptomatic spread, spontaneous recovery and treatment compartments. After fitting our model to the monthly number of new positive tests, we found that the basic reproduction number is approximately $1.0030$. In addition, we derive the endemic equilibrium of the model, which exists if and only if ${\mathcal{R}}_0>1$. The sensitivity analyses of the basic reproduction number and the endemic values of the compartments of treated individuals indicate that infection spreading time can have a significant impact on gonorrhoea spread. Full article

Migration or dispersal of population plays an important role in disease transmission during an outbreak. In this work, we have proposed an SIRS compartmental epidemic model in order to analyze the system dynamics in a two-patch environment. Both the deterministic and fractional order systems have been considered in order to observe the impact of population dispersal. The following analysis has shown that we can have an infected system even if the basic reproduction number in one patch becomes less than unity. Moreover, higher dispersal towards a patch controls the infection level in the other patch to a greater extent. In the optimal control problem (both integer order and fractional), it is assumed that people’s dispersal rate will depend on the disease prevalence, and as such will be treated as a time-dependent control intervention. The numerical results reveal that there is a higher amount of recovery cases in both patches in the presence of optimal dispersal (both integer order and fractional). Not only that, implementation of people’s awareness reduces the infection level significantly even if people disperse at a comparatively higher rate. In a fractional system, it is observed that there will be a higher amount of recovery cases if the order of derivative is less than unity. The effect of fractional order is omnipotent in achieving a stable situation. Full article

The transmission dynamics of onchocerciasis in two interacting populations are examined using a deterministic compartmental model with nonlinear incidence functions. The model undergoes qualitative analysis to examine how it behaves near disease-free equilibrium (DFE) and endemic equilibrium. Using the Lyapunov function, it is demonstrated that the DFE is globally stable when the threshold parameter ${\mathcal{R}}_0\le 1$ is taken into account. When ${\mathcal{R}}_0>1$, it suffices to show globally how asymptotically stable the endemic equilibrium is and its existence. We conduct the bifurcation analysis by looking at the possibility of the model’s equilibria coexisting at ${\mathcal{R}}_0<1$ but near ${\mathcal{R}}_0=1$ using the Center Manifold Theory. We use the sensitivity analysis method to understand how some parameters influence the ${\mathcal{R}}_0$, hence the transmission and mitigation of the disease dynamics. Furthermore, we simulate the model developed numerically to understand the population dynamics. The outcome presented in this article offers valuable understanding of the transmission dynamics of onchocerciasis, specifically in the context of two populations that interact with each other, considering the presence of nonlinear incidence. Full article

The main goal of this work is to propose a novel compartmental SEA (Susceptible–Exposed–Attacked) model to simulate malware spreading on an IoT (Internet of Things) network. This is a deterministic and individual-based model, whose main novelty compared to others lies in the used of continuous mathematical techniques, such as ordinary differential equations, in the description of local transition rules that define the changes of the states of the devices. These states are given by probability vectors representing the probabilities of being susceptible, exposed and attacked at each step of time. The qualitative study of the model is presented, and several simulations are performed. Full article

Given the ongoing migratory crisis in Latin America, we aimed to assess the relationship between human mobility and the spread of yellow fever (YF) in the Darién Gap forest. We investigated how the time taken to cross the forest affects the burden of a potential YF outbreak on people migrating through the forest, the burden on adjacent communities, and the risk to primate biodiversity. Using an SEIR-SEI deterministic compartmental model for humans, monkeys, and vectors, and numerical simulations, we considered the time taken to cross the forest as a measure of exposure. If an outbreak occurs, over 23,000 human cases are projected, with approximately 19,000 infected individuals leaving the forest. Monkeys would also be significantly affected, with the number of human deaths being determined by monkey-related parameters. The pace of crossing the forest is strongly related to the number of exposed and active cases leaving the forest. Panamanian communities must receive support to prepare themselves to protect residents and thousands of people arriving in their territory daily. It would also impact the non-human primate community within the forest, preventing a YF outbreak. This reinforces the importance of a planetary health perspective which reinforces the mutual benefits and connections between efforts to protect human health and conserve biodiversity. Full article

In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible. Full article

In mid-2021, Thailand faced a fourth wave of Coronavirus Disease 2019 (COVID-19) predominantly fueled by the Delta and Alpha variants. The number of cases and deaths rose exponentially, alongside a sharp increase in hospitalizations and intubated patients. The Thai Government then implemented a lockdown to mitigate the outbreak magnitude and prevent cases from overwhelming the healthcare system. This study aimed to model the severity of the outbreak over the following months by different levels of lockdown effectiveness. Secondary analysis was performed on data primarily obtained from the Ministry of Health; the data were analyzed using both the deterministic compartmental model and the system dynamics model. The model was calibrated against the number of daily cases in Greater Bangkok during June–July 2021. We then assessed the outcomes (daily cases, daily deaths, and intubated patients) according to hypothetical lockdowns of varying effectiveness and duration. The findings revealed that lockdown measures could reduce and delay the peak of COVID-19 cases and deaths. A two-month lockdown with 60% effectiveness in the reduction in reproduction number caused the lowest number of cases, deaths, and intubated patients, with a peak about one-fifth of the size of a no-lockdown peak. The two-month lockdown policy also delayed the peak until after December, while in the context of a one-month lockdown, cases peaked during the end of September to early December (depending on the varying degrees of lockdown effectiveness in the reduction in reproduction number). In other words, the implementation of a lockdown policy did not mean the end of the outbreak, but it helped delay the peak. In this sense, implementing a lockdown helped to buy time for the healthcare system to recover and better prepare for any future outbreaks. We recommend further studies that explore the impact of lockdown measures at a sub-provincial level, and examine the impact of lockdowns on parameters not directly related to the spread of disease, such as quality of life and economic implications for individuals and society. Full article

Geospatial vaccine uptake is a critical factor in designing strategies that maximize the population-level impact of a vaccination program. This study uses an innovative spatiotemporal model to assess the impact of vaccination distribution strategies based on disease geospatial attributes and population-level risk assessment. For proof of concept, we adapted a spatially explicit COVID-19 model to investigate a hypothetical geospatial targeting of COVID-19 vaccine rollout in Ohio, United States, at the early phase of COVID-19 pandemic. The population-level deterministic compartmental model, incorporating spatial-geographic components at the county level, was formulated using a set of differential equations stratifying the population according to vaccination status and disease epidemiological characteristics. Three different hypothetical scenarios focusing on geographical subpopulation targeting (areas with high versus low infection intensity) were investigated. Our results suggest that a vaccine program that distributes vaccines equally across the entire state effectively averts infections and hospitalizations (2954 and 165 cases, respectively). However, in a context with equitable vaccine allocation, the number of COVID-19 cases in high infection intensity areas will remain high; the cumulative number of cases remained >30,000 cases. A vaccine program that initially targets high infection intensity areas has the most significant impact in reducing new COVID-19 cases and infection-related hospitalizations (3756 and 213 infections, respectively). Our approach demonstrates the importance of factoring geospatial attributes to the design and implementation of vaccination programs in a context with limited resources during the early stage of the vaccine rollout. Full article