Mobility is a crucial element in comprehending the possible expansion of the transmission chain in an epidemic. In the initial phases, strategies for containing cases can be directly linked to population mobility restrictions, especially when only non-pharmaceutical measures are available. During the pandemic of COVID-19 in Brazil, mobility limitation measures were strongly opposed by a large portion of the population. Hypothetically, if the population had supported such measures, the sharp rise in the number of cases could have been suppressed. In this context, computational modeling offers systematic methods for analyzing scenarios about the development of the epidemiological situation taking into account specific conditions. In this study, we examine the impacts of interstate mobility in Brazil. To do so, we develop a metapopulational model that considers both intra and intercompartmental dynamics, utilizing graph theory. We use a parameter estimation technique that allows us to infer the effective reproduction number in each state and estimate the time-varying transmission rate. This makes it possible to investigate scenarios related to mobility and quantify the effect of people moving between states and how certain measures to limit movement might reduce the impact of the pandemic. Our results demonstrate a clear association between the number of cases and mobility, which is heightened when states are closer to each other. This serves as a proof of concept and shows how reducing mobility in more heavily trafficked areas can be more effective.

OBJECTIVE: 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.

OBJECTIVE: In order to facilitate the tracing of infectious diseases in a small area and to effectively carry out disease control and epidemiological investigations, this research proposes a novel spatiotemporal model to estimate effective reproduction number(Re)for infectious diseases, based on the fundamental concept of contact tracing.
METHODS: This study utilizes the incidence of hand, foot, and mouth disease (HFMD) among children in Bishan District, Chongqing, China from 2015 to 2019. The study incorporates the epidemiological characteristics of HFMD and aims to construct a Spatiotemporal Correlation Discrimination of HFMD. Utilizing ARC ENGINE and C# programming for the creation of a spatio-temporal database dedicated to HFMD to facilitate data collection and analysis. The scientific validity of the proposed method was verified by comparing the effective reproduction number obtained by the traditional SEIR model.
RESULTS: We have ascertained the optimal search radius for the spatiotemporal search model to be 1.5 km. Upon analyzing the resulting Re values, which range from 1.14 to 4.75, we observe a skewed distribution pattern from 2015 to 2019. The median and quartile Re value recorded is 2.42 (1.98, 2.72). Except for 2018, the similarity coefficient r of the years 2015, 2016, 2017, and 2019 were all close to 1, and p <0.05 in the comparison of the two models, indicating that the Re values obtained by using the search model and the traditional SEIR model are correlated and closely related. The results exhibited similarity between the Re curves of both models and the epidemiological characteristics of HFMD. Finally, we illustrated the regional distribution of Re values obtained by the search model at various time intervals on Geographic Information System (GIS) maps which highlighted variations in the incidence of diseases across different communities, neighborhoods, and even smaller areas.
CONCLUSIONS: The model comprehensively considers both temporal variation and spatial heterogeneity in disease transmission and accounts for each individual\'s distinct time of onset and spatial location. This proposed method differs significantly from existing mathematical models used for estimating Re in that it is founded on reasonable scientific assumptions and computer algorithms programming that take into account real-world spatiotemporal factors. It is particularly well-suited for estimating the Re of infectious diseases in relatively stable mobile populations within small geographical areas.

To understand the transmissibility and spread of infectious diseases, epidemiologists turn to estimates of the instantaneous reproduction number. While many estimation approaches exist, their utility may be limited. Challenges of surveillance data collection, model assumptions that are unverifiable with data alone, and computationally inefficient frameworks are critical limitations for many existing approaches. We propose a discrete spline-based approach that solves a convex optimization problem-Poisson trend filtering-using the proximal Newton method. It produces a locally adaptive estimator for instantaneous reproduction number estimation with heterogeneous smoothness. Our methodology remains accurate even under some process misspecifications and is computationally efficient, even for large-scale data. The implementation is easily accessible in a lightweight R package rtestim.

This study presents a computational investigation of a stochastic Zika virus along with optimal control model using the Legendre spectral collocation method (LSCM). By accumulation of stochasticity into the model through the proposed stochastic differential equations, we appropriating the random fluctuations essential in the progression and disease transmission. The stability, convergence and accuracy properties of the LSCM are conscientiously analyzed and also demonstrating its strength for solving the complex epidemiological models. Moreover, the study evaluates the various control strategies, such as treatment, prevention and treatment pesticide control, and identifies optimal combinations that the intervention costs and also minimize the proposed infection rates. The basic properties of the given model, such as the reproduction number, were determined with and without the presence of the control strategies. For R 0 < 0 , the model satisfies the disease-free equilibrium, in this case the disease die out after some time, while for R 0 > 1 , then endemic equilibrium is satisfied, in this case the disease spread in the population at higher scale. The fundamental findings acknowledge the significant impact of stochastic phonemes on the robustness and effectiveness of control strategies that accelerating the need for cost-effective and multi-faceted approaches. In last the results provide the valuable insights for public health department to enabling more impressive mitigation of Zika virus outbreaks and management in real-world scenarios.

Mosquito-borne diseases such as malaria, dengue, Zika, and chikungunya cause significant morbidity and mortality globally, resulting in over 600,000 deaths from malaria and around 36,000 deaths from dengue each year, with millions of people infected annually, leading to substantial economic losses. The existing mosquito control measures, such as long-lasting insecticidal nets (LLINs) and indoor residual spraying (IRS), helped to reduce the infections. However, mosquito-borne diseases are still among the deadliest diseases, forcing us to improve the existing control methods and look for alternative methods simultaneously. Advanced monitoring techniques, including remote sensing, and geographic information systems (GIS) have significantly enhanced the efficiency and effectiveness of mosquito control measures. Mosquitoes\' behavioural traits, such as locomotion, blood-feeding, and fertility are the key determinants of disease transmission and epidemiology. Technological advancements, such as high-resolution cameras, infrared imaging, and artificial intelligence (AI) driven object detection models, including groundbreaking convolutional neural networks, have provided efficient and precise options to monitor various mosquito behaviours, including locomotion, oviposition, fertility, and host-seeking. However, they are not commonly employed in mosquito-based research. This review highlights the novel and significant advancements in behaviour-monitoring tools, mostly from the last decade, due to cutting-edge video monitoring technology and artificial intelligence. These advancements can offer enhanced accuracy, efficiency, and the ability to quickly process large volumes of data, enabling detailed behavioural analysis over extended periods and large sample sizes, unlike traditional manual methods prone to human error and labour-intensive. The use of behaviour-assaying techniques can support or replace existing monitoring techniques and directly contribute to improving control measures by providing more accurate and real-time data on mosquito activity patterns and responses to interventions. This enhanced understanding can help establish the role of behavioural changes in improving epidemiological models, making them more precise and dynamic. As a result, mosquito management strategies can become more adaptive and responsive, leading to more effective and targeted interventions. Ultimately, this will reduce disease transmission and significantly improve public health outcomes.

In epidemiology, realistic disease dynamics often require Susceptible-Exposed-Infected-Recovered (SEIR)-like models because they account for incubation periods before individuals become infectious. However, for the sake of analytical tractability, simpler Susceptible-Infected-Recovered (SIR) models are commonly used, despite their lack of biological realism. Bridging these models is crucial for accurately estimating parameters and fitting models to observed data, particularly in population-level studies of infectious diseases. This paper investigates stochastic versions of the SEIR and SIR frameworks and demonstrates that the SEIR model can be effectively approximated by a SIR model with time-dependent infection and recovery rates. The validity of this approximation is supported by the derivation of a large-population Functional Law of Large Numbers (FLLN) limit and a finite-population concentration inequality. To apply this approximation in practice, the paper introduces a parameter inference methodology based on the Dynamic Survival Analysis (DSA) survival analysis framework. This method enables the fitting of the SIR model to data simulated from the more complex SEIR dynamics, as illustrated through simulated experiments.

Malaria is a fever condition that results from Plasmodium parasites, which are transferred to humans by the attacks of infected female Anopheles mosquitos. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. More so, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The reproduction number R o was determined to be an asymptotically stable condition for disease free and endemic equilibria. In this paper, we used various schemes such as Runge-Kutta order 4 (RK-4) and non-standard finite difference (NSFD). All of the schemes produce different results, but the most appropriate scheme is NSFD. This is true for all step sizes. Various criteria are used in the NSFD scheme to assess the local and global stability of disease-free and endemic equilibrium points. The Routh-Hurwitz condition is used to validate the local stability and Lyapunov stability theorem is used to prove the global asymptotic stability. Global asymptotic stability is proven for the disease-free equilibrium when R 0 ≤ 1 . The endemic equilibrium is investigated for stability when R 0 ≥ 1 . All of the aforementioned schemes and their effects are also numerically demonstrated. The comparative analysis demonstrates that NSFD is superior in every way for the analysis of deterministic epidemic models. The theoretical effects and numerical simulations provided in this text may be used to predict the spread of infectious diseases.

This study introduces a fractional order model to investigate the dynamics of polio disease spread, focusing on its significance, unique results, and conclusions. We emphasize the importance of understanding polio transmission dynamics and propose a novel approach using a fractional order model with an exponential decay kernel. Through rigorous analysis, including existence and stability assessment applying the Caputo Fabrizio fractional operator, we derive key insights into the disease dynamics. Our findings reveal distinct disease-free equilibrium (DFE) and endemic equilibrium (EE) points, shedding light on the disease\'s stability. Furthermore, graphical representations and numerical simulations demonstrate the behavior of the disease under various parameter values, enhancing our understanding of polio transmission dynamics. In conclusion, this study offers valuable insights into the spread of polio and contributes to the broader understanding of infectious disease dynamics.

Fred Brauer was an eminent mathematician who studied dynamical systems, especially differential equations. He made many contributions to mathematical epidemiology, a field that is strongly connected to data, but he always chose to avoid data analysis. Nevertheless, he recognized that fitting models to data is usually necessary when attempting to apply infectious disease transmission models to real public health problems. He was curious to know how one goes about fitting dynamical models to data, and why it can be hard. Initially in response to Fred\'s questions, we developed a user-friendly R package, fitode, that facilitates fitting ordinary differential equations to observed time series. Here, we use this package to provide a brief tutorial introduction to fitting compartmental epidemic models to a single observed time series. We assume that, like Fred, the reader is familiar with dynamical systems from a mathematical perspective, but has limited experience with statistical methodology or optimization techniques.