Compartmental Mathematical Model Research Articles

Modeling with uncertainty quantification reveals the essentials of a non-canonical algal carbon-concentrating mechanism.

The thermoacidophilic red alga Cyanidioschyzon merolae survives its challenging environment likely in part by operating a carbon-concentrating mechanism (CCM). Here, we demonstrated that C. merolae's cellular affinity for CO2 is stronger than the affinity of its rubisco for CO2. This finding provided additional evidence that C. merolae operates a CCM while lacking the structures and functions characteristic of CCMs in other organisms. To test how such a CCM could function, we created a mathematical compartmental model of a simple CCM, distinct from those we have seen previously described in detail. The results of our modeling supported the feasibility of this proposed minimal and non-canonical CCM in C. merolae. To facilitate the robust modeling of this process, we measured and incorporated physiological and enzymatic parameters into the model. Additionally, we trained a surrogate machine learning model to emulate the mechanistic model and characterized the effects of model parameters on key outputs. This parameter exploration enabled us to identify model features that influenced whether the model met the experimentally derived criteria for functional carbon concentration and efficient energy usage. Such parameters included cytosolic pH, bicarbonate pumping cost and kinetics, cell radius, carboxylation velocity, number of thylakoid membranes, and CO2 membrane permeability. Our exploration thus suggested that a non-canonical CCM could exist in C. merolae and illuminated the essential features generally necessary for CCMs to function.

Deciphering Seasonal Patterns in Animal Feeding: A Mechanistic Approach to Analyzing the Restricted Growth of Iberian Pigs.

The growth of animals is influenced by various factors including genetics, nutrition, and environmental conditions. This study focuses on understanding the traditional growth phases of Iberian pigs raised in semi-free-range environments prior to the finishing period within the Mediterranean forest. Using a comprehensive dataset of 5329 pigs, we evaluated the abilities of several mathematical models to predict growth patterns during the early growing and pre-finishing phases. The Gompertz model demonstrated the best fit for the age-weight relationship, indicating its effectiveness in characterizing growth dynamics in these animals. A novel compartmental mathematical model was developed, which integrates age-based estimations for certain body components (protein, water, and ash) with linear body weight predictions for fat. Our findings indicate that this mechanistic model serves as an effective tool for understanding and optimizing management strategies and enhancing growth predictions in traditional pig breeds.

Modelling Citrus Huanglongbing Spread in Scenarios Involving Alternative Hosts, Vector Populations and Removal of Symptomatic Plants

ABSTRACTHuanglongbing (HLB) is the most devastating citrus disease around the world. We have modelled HLB spread in scenarios with different populational levels of the main alternative host (Murraya paniculata) and Diaphorina citri Kuwayama (Asian citrus psyllid—ACP) vector of HLB‐associated bacteria and the removal of HLB‐symptomatic plants. A compartmental deterministic mathematical model was built for representing the HLB dynamics in the Recôncavo Baiano, Bahia State, Brazil. The model encompasses delays on latency and incubation disease periods and on the ACP nymphal stages. The simulations indicated that presence of alternative hosts at a low proportion would not play a crucial role in HLB dynamics in situations of poor ACP management, regardless of HLB‐symptomatic plant eradication. Symptomatic citrus plants contribute more to increase the HLB incidence than the alternative host in scenarios without a suitable ACP management.

A Compartmental Mathematical Model of Novel Coronavirus-19 Transmission Dynamics

A Compartmental Mathematical Model of Novel Coronavirus-19 Transmission Dynamics

Long-term waning of vaccine-induced immunity to measles in England: a mathematical modelling study

Among people infected with measles in England between 2010 and 2019, the proportion of cases who had previously received two doses of vaccine has increased, especially among young adults. Possible explanations include rare infections in vaccinated individuals who did not gain immunity upon vaccination, made more common because fewer individuals in the population were born in the endemic era, before vaccination was introduced, and exposed as part of endemic transmission, or the waning of vaccine-induced immunity, which would present new challenges for measles control in near-elimination settings. We aimed to evaluate whether measles dynamics observed in England between 2010 and 2019 were in line with a waning of vaccine-induced immunity. We used a compartmental mathematical model stratified by age group, region, and vaccine status, fitted to individual-level case data reported in England from 2010 to 2019 and collected by the UK Health Security Agency. The deterministic model was fitted using Monte Carlo Markov Chains under three scenarios: without the waning of vaccine-induced immunity, with waning depending on time since vaccination, and with waning depending on time since vaccination, starting in 2000. We generated stochastic simulations from the fitted parameter sets to evaluate which scenarios could replicate the transmission dynamics observed in vaccinated cases in England. The scenario without waning overestimated the number of one-dose recipients among measles cases, and underestimated the number of two-dose recipients among cases older than 15 years (median 75 cases [95% simulation interval (SI) 44-124] in simulations without waning, 196 [95% SI 122-315] in simulations when waning was included, 188 [95% SI 118-301] in simulations when waning started in 2000, and 202 observed cases). The number of onward transmissions from vaccinated cases was 83% (95% credible interval 72-91%) of the number of transmissions from unvaccinated cases. The estimated waning rate was slow (0·039% per year of age; 95% credible interval 0·034-0·044% per year in the best-fitting scenario with waning starting in 2000), but sufficient to increase measles burden. Measles case dynamics in England are consistent with scenarios assuming the waning of vaccine-induced immunity. Since measles is highly infectious, slow waning leads to a heightened burden in outbreaks, increasing the number of measles cases in people who are both vaccinated and unvaccinated. Our findings show that although the vaccine remains highly protective against measles infections for decades and most transmission is connected to people who are unvaccinated, breakthrough infections are increasingly frequent for individuals aged 15 years and older who have been vaccinated twice. National Institute for Health and Care Research and Wellcome Trust.

An investigation of Susceptible–Exposed–Infectious–Recovered (SEIR) tuberculosis model dynamics with pseudo-recovery and psychological effect

Tuberculosis is one of the most pressing issues of the modern era, posing a severe health risk to humans in recent decades. This study proposes a Susceptible–Exposed–Infectious–Recovered (SEIR) tuberculosis epidemic transmission model with psychological effects and pseudo-recovery. We consider a compartmental mathematical model in which the entire population is divided into four compartments based on their natural features. The model is validated, and parameter values are estimated using Indonesian data from 2002 to 2022. To investigate their epidemiological significance, we proved the positivity and boundedness of solutions, as well as the local and global stability of equilibria. Sensitivity analysis is used to find the most influential parameters with the most significant influence on the basic reproduction number, R0. The bifurcation procedure tools of the center manifold theory are used to conduct a bifurcation study. Mathematical conditions ensure the inferred event of forward bifurcation. We performed numerical simulations that support our theoretical findings.

Exploring Bifurcation in the Compartmental Mathematical Model of COVID-19 Transmission

Exploring Bifurcation in the Compartmental Mathematical Model of COVID-19 Transmission

Assessing vaccine efficacy for infectious diseases with variable immunity using a mathematical model

This study introduces an SIRS compartmental mathematical model encompassing vaccination and variable immunity periods for infectious diseases. I derive a basic reproduction number formula and assess the local and global stability of disease-free and the local stability of the endemic equilibria. I demonstrate that the basic reproduction number in the presence of a vaccine is highly sensitive to the rate of immunity loss, and even a slight reduction in this rate can significantly contribute to disease control. Additionally, I have derived a formula to calculate the critical efficacy period required for a vaccine to effectively manage and control the disease.The analysis conducted for the model suggests that increasing the vaccine’s immunity duration (efficacy) decelerates disease dynamics, leading to reduced rates of reinfection and less severe disease outcomes. Furthermore, this delay contributes to a decrease in the basic reproduction number (R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_0$$\\end{document}), thus facilitating more rapid disease control efforts.

Robustness and exploration between the interplay of the nonlinear co-dynamics HIV/AIDS and pneumonia model via fractional differential operators and a probabilistic approach

In this article, we considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia (H/A-P) co-infection in a human population at different infection stages. Understanding the complexities of co-dynamics is now critically necessary as a consequence. The aim of this research is to construct a co-infection model of H/A-P in the context of fractional calculus operators, white noise and probability density functions, employing a rigorous biological investigation. By exhibiting that the system possesses non-negative and bounded global outcomes, it is shown that the approach is both mathematically and biologically practicable. The required conditions are derived, guaranteeing the eradication of the infection. Furthermore, adequate prerequisites are established, and the configuration is tested for the existence of an ergodic stationary distribution. For discovering the system’s long-term behavior, a deterministic-probabilistic technique for modeling is designed and operated in MATLAB. By employing an extensive review, we hope that the previously mentioned approach improves and leads to mitigating the two diseases and their co-infections by examining a variety of behavioral trends, such as transitions to unpredictable procedures. In addition, the piecewise differential strategies are being outlined as having promising potential for scholars in a range of contexts because they empower them to include particular characteristics across multiple time frame phases. Such formulas can be strengthened via classical techniques, power law, exponential decay, generalized Mittag-Leffler kernels, probability density functions and random procedures. Furthermore, we get an accurate description of the probability density function encircling a quasi-equilibrium point if the effect of H/A-P minimizes the propagation of the co-dynamics. Consequently, scholars can obtain better outcomes when analyzing facts using random perturbations by implementing these strategies for challenging issues. Random perturbations in H/A-P co-infection are crucial in controlling the spread of an epidemic whenever the suggested circulation is steady and the amount of infection eliminated is closely correlated with the random perturbation level.

Estimating the Burden and Distribution of Post-COVID-19 Condition in Washington State, March 2020-October 2023.

After SARS-CoV-2 infection, some people will experience long-term sequelae known as post-COVID-19 condition (PCC). Although PCC is recognized as a public health problem, estimates of the prevalence of PCC are sparse. We described a framework for estimating the incidence and prevalence of PCC by population subgroups and geography over time in Washington State. We collected data on reported COVID-19 cases and hospitalizations and estimated SARS-CoV-2 infections in Washington State from March 2020 through October 2023. The reported case data were incorporated with parameter estimates from published articles and prevalence estimates from the Household Pulse Survey into a mathematical compartmental model of PCC progression. The model used differential equations to describe how the population of people with PCC moved through the model's various stages. This framework allowed us to integrate data on age group, sex, race and ethnicity, vaccination status, and county to estimate incidence and prevalence of PCC for each subgroup. Our model indicated that 6.4% (95% CI, 5.9%-6.8%) of all adults in Washington State were experiencing PCC as of October 2023. In addition to temporal differences in PCC prevalence and incidence, we found substantial differences across age groups, race and ethnicity, and sex. Geographic heterogeneity was pronounced, with the highest rates of PCC in central and eastern Washington. Estimation of PCC prevalence is essential for addressing PCC as a public health problem. Responding to PCC will require continued surveillance, research, and dedicated financial and public health action. This analysis, accounting for heterogeneities, highlights disparities in the prevalence, incidence, and distribution of PCC in Washington State and can better guide awareness and response efforts.

A Mathematical Model of the Dynamics of the Transmission of Monkeypox Disease Using Fractional Differential Equations

AbstractThis study presents a comprehensive analysis of the dynamics of Mpox viral transmission using a compartmental mathematical model. The model incorporates the impact of immunization, isolation, and hospitalization on disease management, as well as the interaction between humans and rodents. Through numerical simulations, the study highlights the effectiveness of isolation in mitigating disease transmission and emphasizes the significance of mathematical modeling and simulation techniques in understanding disease dynamics. The utilization of Caputo's fractional differential equation in the human dynamical model is shown to be effective in regulating disease in all compartments. Sensitivity analysis is conducted to identify the most influential parameters in virus transmission. The findings contribute valuable insights for public health strategies and provide a foundation for further research in disease control and management.

A new COVID-19 variant Kraken: The modeling and analysis of the XBB.1.5 with treatment and immunization control factors

Recent SARS-CoV-2 XBB and BQ subvariants exhibit noticeably enhanced resistance to neutralizing antibodies, including in those persons who are vaccinated and have had breakthrough Omicron infection or who have received the bivalent mRNA booster. Nonlinear dynamics is an intriguing technique for explaining the dynamical behaviors of COVID-19 illness. The goal of this study is to create a novel compartment mathematical model that takes into account populations that have received immunizations against new COVID-19 variants, particularly Omicron. The foundational characteristics of the model, including boundedness and positivity of solutions are established. Following that, the reproduction number has been used to illustrate the equilibrium analysis of steady states. The numerical design of the model has been introduced to assess how various control regimes affect COVID-19 dynamics. All control techniques have been found to have a positive effect on COVID-19 reduction.

Fractional Mathematical Model for Exploring the Influence of Infectious Diseases on Population with Chronic Conditions

AbstractThis paper presents an in‐depth analysis of a hybrid mathematical model, the fractional SECIR model, designed to explore the impact of infectious diseases, with particular emphasis on their effect on individuals with chronic conditions. The study delves into the existence and uniqueness of solutions for the proposed model, yielding several stability results based on parameters that adhere to specific conditions to mitigate pandemic occurrences. The model parameters are estimated using data reported by the Algerian health authorities in recent years, facilitating the application of the model to the Algerian context. The findings derived from the application of this mathematical compartmental model indicate that the basic reproduction number for certain infectious diseases in Algeria (Tuberculosis and COVID‐19) is less than one. This observation suggests the potential for disease eradication or effective management through a combination of targeted interventions including vaccination, high‐quality treatment, and precise isolation measures.

The influence of gender and temephos exposure on community participation in dengue prevention: a compartmental mathematical model

BackgroundThe use of temephos, the most common intervention for the chemical control of Aedes aegypti over the last half century, has disappointing results in control of the infection. The footprint of Aedes and the diseases it carries have spread relentlessly despite massive volumes of temephos. Recent advances in community participation show this might be more effective and sustainable for the control of the dengue vector.MethodsUsing data from the Camino Verde cluster randomized controlled trial, a compartmental mathematical model examines the dynamics of dengue infection with different levels of community participation, taking account of gender of respondent and exposure to temephos.ResultsSimulation of dengue endemicity showed community participation affected the basic reproductive number of infected people. The greatest short-term effect, in terms of people infected with the virus, was the combination of temephos intervention and community participation. There was no evidence of a protective effect of temephos 220 days after the onset of the spread of dengue.ConclusionsMale responses about community participation did not significantly affect modelled numbers of infected people and infectious mosquitoes. Our model suggests that, in the long term, community participation alone may have the best results. Adding temephos to community participation does not improve the effect of community participation alone.

The artificial neural network approach for the transmission of malicious codes in wireless sensor networks with Caputo derivative

AbstractThe current manuscript investigates a six compartmental mathematical model for malicious Codes in Wireless Sensor Network is consider for investigation under the fractional operator of Caputo along with their numerical scheme. The six agent nodes of the network sensors are transferable like in infection with in their community of different nodes. With the help of fixed point theory the presentation of existence and uniqueness of solution of the said model are also given. The scheme of numerical solution under fractional format is developed with the choice of fractional orders which increasing the degree of freedom for such type of network analysis. The numerical simulation of all the six agents are given on different fractional orders along with sensitivity of the fractional orders and some used parameters. The new analysis artificial neural network (ANN) method has been utilized for the considered model and compared with Adams–Bashforth (AB) method. We divided the data set into three categories training, testing and validation with ANN method and the analysis is presented in this work.

Assessing the impact of information-induced self-protection on Zika transmission: A mathematical modeling approach

Abstract As per the World Health Organization’s (WHO’s) suggestions, personal protection via adopting precautionary measures is one of the most effective control aspects to avoid Zika infection in the absence of suitable medical treatment. This personal protection further can be enhanced and explored by propagating information about disease prevalence. Therefore, in this study, we wish to see the effect of information on Zika transmission by formulating a compartmental mathematical model that quantifies the effect of an individual’s behavioral response as self-protection due to information. Furthermore, the basic reproduction number was calculated using the next-generation matrix technique. The model analysis was carried out to determine the local and global stability properties of equilibrium points. In addition, the model shows the occurrence of forward bifurcation when the reproduction number crosses unity. To understand the impact of various model parameters, we conducted a sensitivity analysis using both the normalized sensitivity index and the partial rank correlation coefficient methods. Moreover, we performed numerical simulations to assess the influence of important parameters on the model’s behavior for Zika prevalence. Our study accentuates that as information-induced self-protection increases, the prevalence of Zika infection will be at a very minimum level, and this observation is in line with WHO suggestions.

LOCAL AND GLOBAL STABILITY ANALYSIS OF MEASLES EPIDEMIC MODEL AT DISEASE-FREE EQUILIBRIUM

In this study, a continuous mathematical model for the dynamics of Measles (rubeola) outbreak at constant recruitment rate was formulated. In the model, we partitioned the population into Susceptible (S), Vaccinated (V), exposed (E), Infected (I) and recovered (R) individuals. We analyzed a SVEIR compartmental nonlinear deterministic mathematical model of measles epidemic in a community with constant population. Analytical studies were carried out on the model using the method of linearized stability. The basic reproductive number R0 that governs the disease transmission is obtained from the largest eigenvalue of the next-generation matrix. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if R0<1 and unstable if R0 >1 respectively. Finally, we simulate the model system in MATLAB and obtained the graphical behavior of each compartment. From the simulation, we observed that the measles infection was eradicated in the environment when R0<1.

Numerical simulation shows vaccines’ impact on COVID-19 control: a cautionary tale for spread and control

The purpose of this study was to use a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model to forecast the dynamics of the COVID-19 epidemic in the high and low pandemic cases that occurred in the State of Paraná, Brazil in 2021. Subsequently, the findings of this analysis were compared. The model parameters were adjusted based on official reports from the State of Paraná, Brazil. As a result, it can be observed that the parameters for susceptible population (S) and exposed population (E) tend to decay over time, with a more drastic drop for S and a slower decrease for E in high pandemics. Conversely, the parameter for infected population (I) tends to rise and decay over time, with a tendency to grow in high pandemics. Additionally, the parameter for recovered population (R) tends to rise over time, with a much higher growth rate in low pandemics than in high pandemics, as expected. The numerical simulation appears to align with reality, which is consistent with the scenario in various cities worldwide. Additionally, the implemented model has several advantages, including accurate adjustments despite the simplicity of the hypotheses and projections that are comparable to those of more complex models. The findings presented may provide useful suggestions for the prevention and management of COVID-19 outbreaks in different countries and regions.

The Critical Role of Networks to Describe Disease Spreading Dynamics in Social Systems: A Perspective

This review underscores the critical significance of incorporating networks science in epidemiology. Classic mathematical compartmental models (CMs) employed to describe epidemic spreading may fail to capture the intricacies of real disease dynamics. Rooted in the mean-field assumption, CMs oversimplify by assuming that every individual has the potential to “infect” any other, neglecting the inherent complexity of underlying network structures. Since social interactions follow a networked pattern with specific links between individuals based on social behaviors, joining classic CMs and network science in epidemiology becomes essential for a more authentic portrayal of epidemic spreading. This review delves into noteworthy research studies that, from various perspectives, elucidate how the synergy between networks and CMs can enhance the accuracy of epidemic descriptions. In conclusion, we explore research prospects aimed at further elevating the integration of networks within the realm of epidemiology, recognizing its pivotal role in refining our understanding of disease dynamics.

Stability and Bifurcation Analysis of Measles Model

A six compartmental deterministic mathematical model, governed by a system of ordinary differential equations for measles was formulated in other to study and analyze the transmission dynamics of measles in human population. The model was shown to be mathematically and epidemiologically meaningful. The basic reproduction number of the model was obtained and global stability of the disease-free equilibrium and endemic equilibrium were obtained and shown to be asymptotically stable, whenever the basic reproduction and unstable if otherwise. More so, if then the endemic equilibrium of the model equation is globally asymptotically stable The effect of some parameters of the model relatives to the basic reproduction number was calculated using the normalized forward sensitivity indices, and it was shown that increase in the parameters with negative indices will reduce the value of the basic Reproduction number, while increase in those with positive indices will increase the value of basic reproduction number. The bifurcation analysis was also carried out and the model was shown to exhibit backward bifurcation which indicates that is no longer sufficient for effective disease control. The numerical result shows that isolation of infective plays a major role in reducing the transmission of the disease in the population.