Epidemic Model Research Articles

Strategic investment and program effectiveness: a roadmap to ending AIDS in Bangladesh by 2030

ABSTRACT The journey towards ending AIDS epidemic in Bangladesh by 2030 is ambitious yet achievable. Although Bangladesh has always had a low rate of HIV among its general population, it remains one of seven countries in Asia and the Pacific where new HIV cases are rising. This study evaluates the effectiveness of HIV programmatic strategies and investment scenarios using the AIDS Epidemic Model (AEM) from 2023 to 2030, focusing on optimizing resource allocation and interventions. The findings indicate that without improved program effectiveness, new HIV infections will increase to 1,382 by 2030, failing to meet the targets of the Global AIDS Strategy 2021–2026. If Bangladesh improves its HIV program effectiveness according to the Global AIDS Strategy 2021–2026, the NSP and Global AIDS Strategy targets could significantly lower new infections and AIDS-related deaths and increase treatment coverage to meet Ending AIDS targets. The NSP targets could reduce new HIV infections to under 275 annually and achieve treatment goals by 2030. The study reveals that NSP targets are the most cost-effective, offering the highest benefit-cost ratio, highlighting the urgent need to enhance HIV prevention program effectiveness, particularly among key populations, to achieve both public health and economic benefits.

Optimising HIV spending in 12 eastern European and central Asian countries: a modelling study

The eastern European and central Asian (EECA) region has the fastest growing HIV epidemic globally. We aimed to identify how HIV resources could be allocated for maximum health impact. Between Aug 1 and Dec 23, 2022, allocative efficiency analyses were undertaken for 12 countries in the EECA region (Albania, Armenia, Azerbaijan, Belarus, Georgia, Kazakhstan, Kosovo, Kyrgyzstan, Moldova, Serbia, Tajikistan, and Uzbekistan) using HIV epidemic models developed with Optima HIV. Country models were calibrated to demographic, epidemiological, and programmatic data and validated by national teams. Three scenarios were projected from 2023 to 2030: status quo (continued 2021 spending on HIV programmes); optimised allocation of different spending envelopes to minimise HIV infections and deaths; and achieving 95-95-95 UNAIDS targets by 2030. Aggregated across the 12 models, HIV infections attributable to sexual transmission were estimated to surpass those attributable to transmission through injecting drugs in 2018, with male-to-male sexual transmission accounting for a continuously increasing share. In the status quo scenario, there were an estimated 111 520 (95% CI 28 960-208 270) new HIV infections and 34 530 (17 280-57 410) HIV-related deaths between 2023 and 2030. Aggregated optimisation results suggest that 35 860 (32%) of 111 520 new HIV infections and 9170 (27%) of 34 530 HIV-related deaths could be averted from 2023 to 2030 compared with the status quo, by prioritising antiretroviral therapy and targeted key population programmes. For ten countries, achieving 95% diagnosis was projected to not be possible with the current budget envelope, and for seven countries, this target could require more than three times the current spending. Compared with the status quo, achieving 95-95-95, or as close as possible, could avert 70 880 (64%) of 111 520 new HIV infections and 18 890 (55%) of 34 530 HIV-related deaths from 2023 to 2030. Targeted key population programmes should remain high priorities in the EECA region. Achieving 95-95-95 will require more emphasis on implementing appropriate modes of service delivery that reduce the gap in diagnosis and treatment coverage for people living with HIV. The Global Fund to Fight AIDS, Tuberculosis and Malaria. For the Russian translation of the summary see Supplementary Materials section.

Pulsating waves in a multidimensional reaction-diffusion system of epidemic type

In this work we investigate the existence of front propagation for a two-component reaction -diffusion system of epidemic type posed in a multi-dimensional periodic medium. This system is a spatially heterogeneous version of the well-known Kermack–McKendrick epidemic model with Fickian diffusion. We derive sufficient conditions for the existence of pulsating travelling waves propagating in an arbitrarily given unit direction. Specifically, we prove that the set of admissible wave speeds contains a semi-infinite interval. Then, for each direction of propagation and each admissible speed, there exists a pulsating travelling wave solution of the system which is globally bounded.

Prediction of COVID-19 cases using SIR and AR models: Tokyo-specific and nationwide application

With fast infectious diseases such as COVID-19, the SIR model may not represent the number of infections due to the occurrence of distribution shifts. In this study, we use simulations based on the SIR model to verify the prediction accuracy of new positive cases by considering distribution shifts. Instead of expressing the overall number of new positive cases in the SIR model, the number of new positive cases in a specific region is simulated, the expanded estimation ratio is expressed in the AR model, and these are multiplied to predict the overall number. In addition to the parameters used in the SIR model, we introduced parameters related to social variables. The parameters for the simulation were estimated daily from the data using approximate Bayesian computation (ABC). Using this method, the average absolute percent error in predicting the number of positive cases for the peak of the eighth wave (2022/12/22–12/28) for all of Japan was found to be 62.2% when using data up to two months before the peak and 6.2% when using data up to one month before the peak. Our simulations based on the SIR model reproduced the number of new positive cases across Japan and produced reasonable results when predicting the peak of the eighth wave.

Design of Epidemic Model For Covid-19 Disease Prediction Using Deep Learning

Promising technologies are available in the developing field of Public Health Surveillance (PHS) to help public health authorities make decisions more quickly by expediting the process of monitoring, analysing, and using unofficial sources. The cornerstone of public health practice is public health surveillance. Influencing policy decisions, spearheading new program initiatives, improving public relations, and helping organisations assess their research expenditures all depend on surveillance data. Public health experts may find that mathematical models are an effective tool in controlling epidemics, which might result in a significant drop in the number of cases and deaths. Moreover, decision-makers can optimise prospective control strategies, including as vaccination campaigns, lockdowns, and containment measures, by using mathematical models to produce long- and short-term forecasts. This work suggests the evolution of epidemics.

Simplicial epidemic model with a threshold policy

We establish a simplicial empty-susceptible–infected (ESI) model with consideration of threshold policy to depict the network-based epidemic transmission, where the underlying propagation structures are expanded from edges to higher-order structures. To address the epidemic evolution in an explicit network, we formulate the quenched mean-field probability evolution about each site, which is composed of non-smooth differential equations based on network topology. Remarkably, under the combined action of non-smooth and high-order structures, a tristable state is observed in empirical social networks, which is consistent with the coexistence of three stable equilibria by analysis of the mean-field system. Moreover, we find that a sliding mode exists in empirical social networks, which is also indicated by the theoretical analysis of the mean-field probability equations. Finally, the system is divided into the free subsystem without the threshold policy and control subsystem with the threshold policy. Both subsystems admit a stable disease-free equilibrium and a stable endemic equilibrium, as well as coexistence of a stable disease-free equilibrium and a stable pseudo equilibrium in the system, thereby admitting three types of the bistable state under the policy with different critical levels.

On the use of reactive multiparticle collision dynamics to gather particulate level information from simulations of epidemic models

This paper discusses the application of reactive multiparticle collision (RMPC) dynamics, a particle-based method, to epidemic models. First, we consider a susceptible-infectious-recovered framework to obtain data on contacts of susceptibles with infectious people in a population. It is found that the number of contacts increases and the contact duration decreases with increases in the disease transmission rate and average population speed. Next, we obtain reinfection statistics for a general infectious disease from RMPC simulations of a susceptible-infectious-recovered-susceptible model. Finally, we simulate a susceptible-exposed-infectious-recovered model and gather the exposure, infection, and recovery time for the individuals in the population under consideration. It is worth mentioning that we can collect data in the form of average contact duration, average initial infection time, etc., from RMPC simulations of these models, which is not possible with population-based stochastic models, or deterministic systems. This study provides quantitative insights on the potential of RMPC to simulate epidemic models and motivates future efforts for its application in the field of mathematical epidemiology.

A spatio-temporal infection epidemic model with fractional order, general incidence, and vaccination analysis

The paper investigates a spatio-temporal SEIR epidemic model on a global level with fractional order. It employs four partial differential equations incorporating fractional derivatives and account for diffusion to characterize infection dynamics. By applying fixed-point theorem results, the paper establishes the existence, uniqueness, and boundedness of the solution. Equilibrium points are determined based on vaccination values and the basic reproduction number R0. Global stability of each equilibrium is confirmed using the Lyapunov direct method. Through simulations with a predictor–corrector algorithm, key insights into epidemiological dynamics are provided, elucidating the impact of vaccination on reducing disease transmission and altering R0. Trajectories of various compartments closely align with theoretical equilibrium points, affirming the model’s predictive precision. Furthermore, simulations indicate the potential for attaining disease-free equilibria with heightened vaccination rates, underscoring the pivotal role of vaccination strategies in epidemic control and disease eradication. It was shown that the fractional derivative order has no effect on the equilibrium stability but rather only on the convergence speed towards the equilibrium points.

Temporal Dynamics and Interplay of Transmission Rate, Vaccination, and Mutation in Epidemic Modeling: A Poisson Point Process Approach

Temporal Dynamics and Interplay of Transmission Rate, Vaccination, and Mutation in Epidemic Modeling: A Poisson Point Process Approach

Asymptotic Analysis of a Delayed SVIR Epidemic Model with Immigration

Asymptotic Analysis of a Delayed SVIR Epidemic Model with Immigration

A cholera model coupling within-host and between-host with age-dependent and asymptomatic infections

In this paper, a coupling cholera epidemic model is proposed, in which the pathogens could both spread within-host and between-host, meanwhile, there exist age-dependent infection between the asymptomatic and symptomatic infected people. For the fast-time subsystem, the infection-free and endemic equilibria are both globally asymptotically stable. For the slow-time subsystem, the basic reproduction number R0 is determined, by which we observe that the disease-free equilibrium is globally asymptotically stable (the absence of pathogens in environment) if R0<1, while the endemic equilibrium is globally asymptotically stable (the presence of pathogens in environment) when R0>1. The theoretical results are illustrated by numerical simulations, by which we find that age-dependent and asymptomatic infections may further promote cholera spread. Besides, the linking of pathogen transmission at the individual level with infection at the population level could result in forward or backward bifurcation.

Dynamical behavior of a fractional-order epidemic model for investigating two fear effect functions

Using the Caputo operator, a model for a fractional-order epidemic is developed to investigate the fear effect in a pathogenic environment and vaccination procedure. First, we examine if the proposed model is positive. Next, based on the value of the control reproduction number Rc, we compute both the control reproduction and strength numbers and derive the stability criteria of the disease-free equilibrium. In fact, we use the comparison theorem to show that the disease-free equilibrium point is globally asymptotically stable whenever Rc<1. Next, we prove that the solutions of the fractional model exist and are unique. Finally, several numerical simulations are conducted to verify our theoretical results.

Global Dynamics and Optimal Control of a Fractional-Order SIV Epidemic Model with Nonmonotonic Occurrence Rate

This paper performs a detailed analysis and explores optimal control strategies for a fractional-order SIV epidemic model, incorporating a nonmonotonic incidence rate. In this paper, the population of vaccinated individuals is included in the disease dynamics model. After proving the non-negative boundedness of the fractional-order SIV model, we focus on analyzing the equilibrium point characteristics of the model, delving into its existence, uniqueness, and stability analysis. In addition, our research includes formulating optimal control strategies specifically aimed at minimizing the number of infections while keeping costs as low as possible. To validate the theoretical findings and uncover the practical efficacy and prospects of control measures in mitigating epidemic spread, numerical simulations are performed.

A Sensitivity Analysis of the PSITPS Epidemic Model’s Parameters for COVID-19

Given the prevailing circumstances surrounding the transmission of COVID-19, which has been classified as a worldwide epidemic by the World Health Organization, a sensitivity analysis was performed on the Protected-Susceptible-Infected-Treated- Protected- Susceptible ( ) epidemic model. The objective of this analysis was to identify the specific parameters associated with the basic reproduction number that contribute to the propagation of the COVID-19 epidemic in Najaf. The findings indicate that the sensitivity index of parameters exhibiting a positive sign is positively correlated with the extent of the epidemic's spread in Najaf. Conversely, parameters displaying a negative sign are inversely correlated with the spread of the epidemic. The analysis was conducted numerically using MATLAB to confirm the results of the study.

An unconditional boundary and dynamics preserving scheme for the stochastic epidemic model

An unconditional boundary and dynamics preserving scheme for the stochastic epidemic model

Global insights into a stochastic SIRS epidemic model with Beddington–DeAngelis incidence rate

Global insights into a stochastic SIRS epidemic model with Beddington–DeAngelis incidence rate

Dynamics of a multi-strain HIV/AIDS epidemic model with treatment and its adherence

Dynamics of a multi-strain HIV/AIDS epidemic model with treatment and its adherence

Erratum: Heterogeneity can markedly increase final outbreak size in the SIR model of epidemics [Phys. Rev. Research 6 , 012010 (2024)

Erratum: Heterogeneity can markedly increase final outbreak size in the SIR model of epidemics [Phys. Rev. Research <b>6</b> , 012010 (2024)

Global stability analysis, stabilization and synchronization of an SEIR epidemic model

In this paper, we investigate an SEIR epidemic model in which recruitment is assumed to be regulated by a constant function. The SEIR model is a widely-used epidemiological framework that categorises the population into four distinct groups: Susceptible, Exposed, Infectious, and Removed. It employs a system of differential equations to describe the transitions of individuals among these groups, making it a valuable tool for understanding and modelling the dynamics of infectious diseases. Mathematical analysis is used to study the dynamic behaviour of this model. We first determine the basic reproduction number, denoted as R 0 , which governs the dynamics of the SEIR model. Our findings reveal that when R 0 is less than 1, the unique disease-free equilibrium is asymptotically stable, and there is no endemic equilibrium. However, when R 0 exceeds 1, the disease-free equilibrium becomes unstable, and a unique, asymptotically stable endemic equilibrium emerges. Furthermore, by constructing appropriate Lyapunov functions, we have studied the global asymptotic stability of the two equilibrium points. On the other hand, we have used the backstepping method to design a control law that stabilises the SEIR model towards the disease-free equilibrium, which means the eradication of the disease from the target population. Next, we have used the same method to synchronise the SEIR drive system and the SEIR response system. This method is used to stabilise the synchronisation error dynamics arising from the mismatch between the drive and response systems. Finally, we presented numerical simulations to illustrate the theoretical results.

To secure an e‐commerce system using epidemic mathematical modeling with neural network

SummarySecuring an e‐commerce system using epidemic mathematical modeling with neural networks involves adapting epidemiological principles to combat the spread of misinformation. Just like how epidemiologists track the spread of diseases through populations, we can track the dissemination of fake news through online platforms. By modeling how fake news spreads, we gain insights into its propagation patterns, enabling us to develop more effective countermeasures. Neural networks, with their ability to learn from data, play a crucial role in this process by analyzing vast amounts of information to identify and mitigate the impact of fake news. One potential disadvantage of using epidemic mathematical modeling with neural networks to secure e‐commerce systems is the complexity of the approach. The epidemic‐based recurrent long short‐term memory (E‐RLSTM) technique addresses the complexity and evolving nature of fake news propagation by leveraging the strengths of recurrent neural networks (RNNs), specifically long short‐term memory (LSTM) units, within an epidemic modeling framework. One advantage of using epidemic mathematical modeling with neural networks to secure e‐commerce systems is its proactive nature. One significant finding in employing this approach is the ability to uncover hidden connections and correlations within the data. E‐RLSTM stands out by capturing temporal dynamics and integrating epidemic parameters into its LSTM architecture, ensuring robustness and adaptability in detecting and combating fake news within e‐commerce systems, outperforming other techniques in accuracy and performance. Description of the NSL‐KDD dataset offers easy access to a valuable repository for benchmarking cyber security. Contained within are more than 120,000 authentic samples of cyber‐attacks across 41 distinct categories, providing an excellent environment for testing intrusion detection systems.