Latent Compartments Research Articles

Stability and bifurcations for a 3D Filippov SEIS model with limited medical resources

In this paper, a three-dimensional (3D) Filippov SEIS epidemic model is proposed to characterize the impact of limited medical resources on disease transmission with discontinuous treatment functions. Qualitative analysis of non-smooth dynamical behaviors are performed on two subsystems and sliding modes. Criteria on the stability of various kinds of feasible equilibria and bifurcations, e.g., saddle-node bifurcation, transcritical bifurcation, and boundary equilibrium bifurcation, are established. The theoretical results are illustrated by numerical simulation, from which we find there could exist bistable phenomena, e.g., endemic and pseudo-equilibria, endemic equilibria of the two subsystems, or endemic and disease-free equilibria, even the basic reproduction numbers of two subsystems are less than 1. The disease spread is dependent both on the limited medical resources and latent compartment, which are more beneficial to effective disease control than planar Filippov and smooth models.

Epidemiological modeling of Influenza-Like Illness (ILI) transmission in Jakarta, Indonesia through cumulative generating operator on SLIR model

Influenza-Like Illness (ILI) constitutes a significant global health concern characterized by its high infection rates and widespread distribution worldwide. While influenza viruses, primarily types A and B, are primary contributors to ILI cases, other respiratory viruses also play a role in its prevalence. Jakarta, Indonesia’s largest and densely populated city, has consistently reported a notable weekly number of ILI cases from 2016 to mid-2022. Intriguingly, this pattern of cases is irregular and does not exhibit a direct association with seasonal climate fluctuations. In response to this complex scenario, we have developed a SLIR mathematical model featuring a cumulative generating operator in the form of a multiple-terms sigmoid function, obtained from weekly cumulative data to derive model solutions. A total of 12 terms within the sigmoid function yielded a decent fit to the actual data spanning 339 weeks. Our correlation analysis unveiled distinct temporal relationships within the model, revealing an 8-week time lag between the dynamics of the infection rate and the latent compartment, along with a 2-week lag marking the incubation period between the latent and infected compartments. Furthermore, the effective reproduction number displayed recurrent fluctuations around a threshold of 1, indicating the endemic characteristics where infection persists within the population. This in-depth comprehension of ILI transmission dynamics and effective reproduction numbers plays a significant role in devising control measures and informed policy-making decisions.

Global behaviour of a tuberculosis model with difference in awareness and treatment adherence levels

The treatment adherence level of tuberculosis patients is critically related to their awareness level about tuberculosis and anti-tuberculosis therapy. Tuberculosis is always spreading if the community has low level of awareness. In this article a mathematical model describing the impact of treatment adherence and difference in awareness level on tuberculosis transmission dynamics is investigated. It is assumed that the detected infectious individuals with low level of awareness after treatment may enter either the recovered compartment due to treatment adherence or the latent compartment due to lack of adherence. We compute the epidemic threshold parameter, Rb, to study its role on the dynamics and stability of the proposed model. Mathematical analyses of this model reveal that treatment nonadherence of individuals with active tuberculosis may lead to relapse. Analysis of the epidemic threshold parameter shows that increase in awareness level, treatment and adherence to medication has a positive effect on tuberculosis control. Whereas, decrease in effective contact rate and endogenous reactivation rate help to reduce tuberculosis infection. The numerical simulations of the model illustrate the feasibility of our analytical conclusions.

Inference on the dynamics of COVID-19 in the United States

The evolution of the COVID-19 pandemic is described through a time-dependent stochastic dynamic model in discrete time. The proposed multi-compartment model is expressed through a system of difference equations. Information on the social distancing measures and diagnostic testing rates are incorporated to characterize the dynamics of the various compartments of the model. In contrast with conventional epidemiological models, the proposed model involves interpretable temporally static and dynamic epidemiological rate parameters. A model fitting strategy built upon nonparametric smoothing is employed for estimating the time-varying parameters, while profiling over the time-independent parameters. Confidence bands of the parameters are obtained through a residual bootstrap procedure. A key feature of the methodology is its ability to estimate latent unobservable compartments such as the number of asymptomatic but infected individuals who are known to be the key vectors of COVID-19 spread. The nature of the disease dynamics is further quantified by relevant epidemiological markers that make use of the estimates of latent compartments. The methodology is applied to understand the true extent and dynamics of the pandemic in various states within the United States (US).

Simulating within host human immunodeficiency virus 1 genome evolution in the persistent reservoir.

The complexities of viral evolution can be difficult to elucidate. Software simulating viral evolution provides powerful tools for exploring hypotheses of viral systems, especially in situations where thorough empirical data are difficult to obtain or parameters of interest are difficult to measure. Human immunodeficiency virus 1 (HIV-1) infection has no durable cure; this is primarily due to the virus’ ability to integrate into the genome of host cells, where it can remain in a transcriptionally latent state. An effective cure strategy must eliminate every copy of HIV-1 in this ‘persistent reservoir’ because proviruses can reactivate, even decades later, to resume an active infection. However, many features of the persistent reservoir remain unclear, including the temporal dynamics of HIV-1 integration frequency and the longevity of the resulting reservoir. Thus, sophisticated analyses are required to measure these features and determine their temporal dynamics. Here, we present software that is an extension of SANTA-SIM to include multiple compartments of viral populations. We used the resulting software to create a model of HIV-1 within host evolution that incorporates the persistent HIV-1 reservoir. This model is composed of two compartments, an active compartment and a latent compartment. With this model, we compared five different date estimation methods (Closest Sequence, Clade, Linear Regression, Least Squares, and Maximum Likelihood) to recover the integration dates of genomes in our model’s HIV-1 reservoir. We found that the Least Squares method performed the best with the highest concordance (0.80) between real and estimated dates and the lowest absolute error (all pairwise t tests: P < 0.01). Our software is a useful tool for validating bioinformatics software and understanding the dynamics of the persistent HIV-1 reservoir.

Modeling the transmission dynamics of tuberculosis in Khyber Pakhtunkhwa Pakistan

This article addresses the dynamics of the bacterial disease tuberculosis in Khyber Pakhtunkhwa, Pakistan, through a mathematical model. In this work, the latent compartment is divided into slow and fast kinds of progresses. The model is parameterized based on the reported tuberculosis-infected cases in Khyber Pakhtunkhwa for the period 2002–2017. We obtain the basic reproduction number [Formula: see text] of the model using the next-generation method. The estimated value of [Formula: see text] for the given period is approximately 1.38. Furthermore, it is shown that the model has two types of equilibria: disease-free and endemic equilibriums. The global stability analysis of the model equilibria is shown via Lyapunov functions. We also perform the sensitivity analysis of [Formula: see text] and present their corresponding graphical results to examine the relative importance of various model parameters to tuberculosis transmission and prevalence. Finally, some numerical simulations are done for the estimated parameters and the key parameters effects are considered on the curtailing tuberculosis disease. From the numerical results and model sensitivity analysis, it is found that the spread of tuberculosis can be minimized by increasing the treatment rate [Formula: see text] of infected people and decreasing the effective disease transmission rate [Formula: see text] and the rate [Formula: see text] at which the individuals leave treated class reenter infected classes.

Global dynamics of a tuberculosis transmission model with age of infection and incomplete treatment

In this paper, a mathematical model describing tuberculosis transmission with incomplete treatment and continuous age structure for latently infected and infectious individuals is investigated. It is assumed in the model that the treated individuals may enter either the latent compartment due to the remainder of Mycobacterium tuberculosis or the infectious compartment due to the treatment failure. It is shown that the global transmission dynamics of the disease is fully determined by the basic reproduction number. The asymptotic smoothness of the semi-flow generated by the system is established. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state of the model is established. By using the persistence theory for infinite dimensional system, the uniform persistence of the system is established when the basic reproduction number is greater than unity. By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proven that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable; if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable.

Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment

The mathematical model for analyzing the transmission dynamics of HIV/AIDS epidemic with treatment is studied by considering the three latent compartments for slow, medium and fast progresses of developing the AIDS. By constructing the system of differential equations for the different population groups namely susceptible, three types of latent individuals, symptomatic stage group and full blown AIDS individuals, the mathematical analysis is carried out in order to understand the dynamics of disease spread. By determining the basic reproduction number (R₀), the model examines the two equilibrium points (i) the disease free equilibrium and (ii) the endemic equilibrium. It is established that if <i>R₀ &lt;1</i>, the disease free equilibrium is locally and globally asymptotically stable. The stability of endemic equilibrium has also been discussed.

Dissecting seipin function: the localized accumulation of phosphatidic acid at ER/LD junctions in the absence of seipin is suppressed by Sei1p(ΔNterm) only in combination with Ldb16p.

BackgroundSeipin is required for the correct assembly of cytoplasmic lipid droplets. In the absence of the yeast seipin homolog Sei1p (formerly Fld1p), droplets are slow to bud from the endoplasmic reticulum, lack the normal component of proteins on their surface, are highly heterogeneous in size and shape, often bud into the nucleus, and promote local proliferation of the endoplasmic reticulum in which they become tangled. But the mechanism by which seipin catalyzes lipid droplet formation is still uncertain.ResultsSeipin prevents a localized accumulation of phosphatidic acid (PA puncta) at ER-droplet junctions. PA puncta were detected with three different probes: Opi1p, Spo20p(51–91) and Pah1p. A system of droplet induction was used to show that PA puncta were not present until droplets were formed; the puncta appeared regardless of whether droplets consisted of triacylglycerol or steryl ester. Deletion strains were used to demonstrate that a single phosphatidic acid-producing enzyme is not responsible for the generation of the puncta, and the puncta remain resistant to overexpression of enzymes that metabolize phosphatidic acid, suggesting that this lipid is trapped in a latent compartment. Suppression of PA puncta requires the first 14 amino acids of Sei1p (Nterm), a domain that is also important for initiation of droplet assembly. Consistent with recent evidence that Ldb16p and Sei1p form a functional unit, the PA puncta phenotype in the ldb16Δ sei1Δ strain was rescued by human seipin. Moreover, PA puncta in the sei1Δ strain expressing Sei1pΔNterm was suppressed by overexpression of Ldb16p, suggesting a functional interaction of Nterm with this protein. Overexpression of both Sei1p and Ldb16p, but not Sei1p alone, is sufficient to cause a large increase in droplet number. However, Ldb16p alone increases triacylglycerol accumulation in the ldb16Δ sei1Δ background.ConclusionWe hypothesize that seipin prevents formation of membranes with extreme curvature at endoplasmic reticulum/droplet junctions that would attract phosphatidic acid. While Ldb16p alone can affect triacylglycerol accumulation, proper droplet formation requires the collaboration of Sei1p and Ldb16.Electronic supplementary materialThe online version of this article (doi:10.1186/s12860-015-0075-3) contains supplementary material, which is available to authorized users.

Zoonotic Visceral Leishmania: Modeling and Control

In this work we focus on the transmission dynamics of Visceral strains of leishmania, using mathematical model with two latent compartments in human. From the governing differential equations of the model, we find the reproductive number R0; the number of secondary infection and its biological interpretation. Using Routh- Hurwitz criteria on upper bound matrix, the threshold condition, for stability of the Disease Free State, is calculated. Finally we show that the disease free equilibrium is globally asymptotically stable if R0<<ξ 11.

Global stability for an HIV/AIDS epidemic model with different latent stages and treatment

An HIV/AIDS epidemic model with different latent stages and treatment is constructed. The model allows for the latent individuals to have the slow and fast latent compartments. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are determined by the basic reproduction number under some conditions. If R0<1, the disease free equilibrium is globally asymptotically stable, and if R0>1, the endemic equilibrium is globally asymptotically stable for a special case. Some numerical simulations are also carried out to confirm the analytical results.

A meta-analysis of the effect of dose and age at exposure on shedding ofMycobacterium aviumsubspeciesparatuberculosis(MAP) in experimentally infected calves and cows

A meta-analysis was performed using all published and one unpublished long-term infection-challenge experiments to quantify the age- and dose-dependence of early and late shedding of Mycobacterium avium subsp. paratuberculosis (MAP) in cattle. There were 194 animals from 17 studies that fulfilled the inclusion criteria, of which 173 received a known dose of MAP and 21 were exposed naturally. Results from parametric time-to-event models indicated that challenging older calves or using multiple-exposure experimental systems resulted in a smaller proportion and shorter duration of early shedding as well as slower transition to late shedding from latent compartments. Calves exposed naturally showed variable infection progression rates, not dissimilar to other infection routes. The log-normal distribution was most appropriate for modelling infection-progression events. The infection pattern revealed by the modelling allowed better understanding of low-grade endemicity of MAP in cattle, and the parameter estimates are the basis for future transmission dynamics modelling.

Global stability of two models with incomplete treatment for tuberculosis

Two tuberculosis (TB) models with incomplete treatment are investigated. It is assumed that the treated individuals may enter either the latent compartment due to the remainder of Mycobacterium tuberculosis or the infectious compartment due to the treatment failure. The first model is a simple one with treatment failure reflecting the current TB treatment fact in most countries with high tuberculosis incidence. The second model refines the simple one by dividing the latent compartment into slow and fast two kinds of progresses. This improvement can be used to describe the case that the latent TB individuals have been infected with some other chronic diseases (such as HIV and diabetes) which may weaken the immunity of infected individuals and shorten the latent period of TB. Both of the two models assume mass action incidence and exponential distributions of transfers between different compartments. The basic reproduction numbers of the two models are derived and their intuitive epidemiological interpretations are given. The global dynamics of two models are all proved by using Liapunov functions. At last, some strategies to control the spread of tuberculosis are discussed.

Establishment of Latent HIV-1 Infection of Resting CD4+ T Lymphocytes Does Not Require Inactivation of Vpr

The introduction of highly active antiretroviral therapy (HAART) for the treatment of HIV-1 infection has allowed dramatic reductions in plasma virus levels to below the limit of detection in many patients. However, latently infected CD4+ memory T lymphocytes persist as an important reservoir for the virus in the presence of this aggressive therapy and represent a major barrier to HIV-1 eradication with HAART. The mechanism through which the latent compartment is formed has not yet been established. It may involve actively proliferating CD4+ T-cell intermediates that are infected with HIV-1 and revert back to a resting state, carrying integrated provirus at some low frequency. The HIV-1 accessory protein Vpr, which mediates G2 cell cycle arrest in host cells, may interfere with the formation of the latently infected T cells by preventing them from exiting the cell cycle to return to a resting state. To investigate the role of the Vpr in the formation of latently infected memory T cells, we cloned and characterized vpr genes from viruses in the latent reservoir. Both sequence analysis and functional assays demonstrated that the vpr gene products of the viruses isolated from the latent pool did not differ significantly from those of a functional Vpr (NL4-3). These results indicate that the generation of resting G0 memory T lymphocytes that carry latent HIV-1 provirus occurs despite the G2 arrest function of the vpr gene product.