Multi-strain Model Research Articles

Impact of antigen test target failure and testing strategies on the transmission of SARS-CoV-2 variants

Population testing remains central to COVID-19 control and surveillance, with countries increasingly using antigen tests rather than molecular tests. Here we describe a SARS-CoV-2 variant that escapes N antigen tests due to multiple disruptive amino-acid substitutions in the N protein. By fitting a multistrain compartmental model to genomic and epidemiological data, we show that widespread antigen testing in the Italian region of Veneto favored the undetected spread of the antigen-escape variant compared to the rest of Italy. We highlight novel limitations of widespread antigen testing in the absence of molecular testing for diagnostic or confirmatory purposes. Notably, we find that genomic surveillance systems which rely on antigen population testing to identify samples for sequencing will bias detection of escape antigen test variants. Together, these findings highlight the importance of retaining molecular testing for surveillance purposes, including in contexts where the use of antigen tests is widespread.

Global dynamics of two-strain epidemic model with single-strain vaccination in complex networks

Contagious pathogens, such as influenza and COVID-19, are known to be represented by multiple genetic strains. Different genetic strains may have different characteristics, such as spreading more easily, causing more severe diseases, or even evading the immune response of the host. These facts complicate our ability to combat these diseases. There are many ways to prevent the spread of infectious diseases, and vaccination is the most effective. Thus, studying the impact of vaccines on the dynamics of a multi-strain model is crucial. Moreover, the notion of complex networks is commonly used to describe the social contacts that should be of particular concern in epidemic dynamics. In this paper, we investigate a two-strain epidemic model using a single-strain vaccine in complex networks. We first derive two threshold quantities, R1 and R2, for each strain. Then, by using the basic tools for stability analysis in dynamical systems (i.e., Lyapunov function method and LaSalle’s invariance principle), we prove that if R1<1 and R2<1, then the disease-free equilibrium is globally asymptotically stable in the two-strain model. This means that the disease will die out. Furthermore, the global stability of each strain dominance equilibrium is established by introducing further critical values. Under these stability conditions, we can determine which strain will survive. Particularly, we find that the two strains can coexist under certain condition; thus, a coexistence equilibrium exists. Moreover, as long as the equilibrium exists, it is globally stable. Numerical simulations are conducted to validate the theoretical results.

A Stochastic Multi-Strain SIR Model with Two-Dose Vaccination Rate

Infectious diseases remain a substantial public health concern as they are among the leading causes of death. Immunization by vaccination can reduce the infectious diseases-related risk of suffering and death. Many countries have developed COVID-19 vaccines in the past two years to control the COVID-19 pandemic. Due to an urgent need for COVID-19 vaccines, the vaccine administration of COVID-19 is in the mode of emergency use authorization to facilitate the availability and use of vaccines. Therefore, the vaccine development time is extraordinarily short, but administering two doses is generally recommended within a specific time to achieve sufficient protection. However, it may be essential to identify an appropriate interval between two vaccinations. We constructed a stochastic multi-strain SIR model for a two-dose vaccine administration to address this issue. We introduced randomness into this model mainly through the transmission rate parameters. We discussed the uniqueness of the positive solution to the model and presented the conditions for the extinction and persistence of disease. In addition, we explored the optimal cost to improve the epidemic based on two cost functions. The numerical simulations showed that the administration rate of both vaccine doses had a significant effect on disease transmission.

A multi-strain epidemic model for COVID-19 with infected and asymptomatic cases: Application to French data

Many SARS-CoV-2 variants have appeared over the last months, and many more will continue to appear. Understanding the competition between these different variants could help make future predictions on the evolution of epidemics. In this study we use a mathematical model to investigate the impact of three different SARS-CoV-2 variants on the spread of COVID-19 across France, between January-May 2021 (before vaccination was extended to the full population). To this end, we use the data from Geodes (produced by Public Health France) and a particle swarm optimisation algorithm, to estimate the model parameters and further calculate a value for the basic reproduction number R0. Sensitivity and uncertainty analysis is then used to better understand the impact of estimated parameter values on the number of infections leading to both symptomatic and asymptomatic individuals. The results confirmed that, as expected, the alpha, beta and gamma variants are more transmissible than the original viral strain. In addition, the sensitivity results showed that the beta/gamma variants could have lead to a larger number of infections in France (of both symptomatic and asymptomatic people).

Dynamics of COVID-19 in Amazonia: A history of government denialism and the risk of a third wave

The city of Manaus (the capital of Brazil’s state of Amazonas) has become a key location for understanding the dynamics of the global pandemic of COVID-19. Different groups of scientists have foreseen different scenarios, such as the second wave or that Manaus could escape such a wave by having reached herd immunity. Here we test five hypotheses that explain the second wave of COVID-19 in Manaus: 1) The greater transmissibility of the Amazonian (gamma or P.1) variant is responsible for the second wave; 2) SARS-CoV-2 infection levels during the first wave were overestimated by those foreseeing herd immunity, and the population remained below this threshold when the second wave began at the beginning of December 2020; 3) Antibodies acquired from infection by one lineage do not confer immunity against other lineages; 4) Loss of immunity has generated a feedback phenomenon among infected people, which could generate future waves, and 5) A combination of the foregoing hypotheses. We also evaluated the possibility of a third wave in Manaus despite advances in vaccination, the new wave being due to the introduction of the delta variant in the region and the loss of immunity from natural contact with the virus. We developed a multi-strain SEIRS (Susceptible-Exposed-Infected-Removed-Susceptible) model and fed it with data for Manaus on mobility, COVID-19 hospitalizations, numbers of cases and deaths. Our model contemplated the current vaccination rates for all vaccines applied in Manaus and the individual protection rates already known for each vaccine. Our results indicate that the SARS-CoV-2 gamma (P.1) strain that originated in the Amazon region is not the cause of the second wave of COVID-19 in Manaus, but rather this strain originated during the second wave and became predominant in January 2021. Our multi-strain SEIRS model indicates that neither the doubled transmission rate of the gamma variant nor the loss of immunity alone is sufficient to explain the sudden rise of hospitalizations in late December 2020. Our results also indicate that the most plausible explanation for the current second wave is a SARS-CoV-2 infection level at around 50% of the population in early December 2020, together with loss of population immunity and early relaxation of restrictive measures. The most-plausible model indicates that contact with one strain does not provide protection against other strains and that the gamma variant has a transmissibility rate twice that of the original SARS-CoV-2 strain. Our model also shows that, despite the advance of vaccination, and even if future vaccination advances at a steady pace, the introduction of the delta variant or other new variants could cause a new wave of COVID-19.

Equitable access to COVID-19 vaccines makes a life-saving difference to all countries

Despite broad agreement on the negative consequences of vaccine inequity, the distribution of COVID-19 vaccines is imbalanced. Access to vaccines in high-income countries (HICs) is far greater than in low- and middle-income countries (LMICs). As a result, there continue to be high rates of COVID-19 infections and deaths in LMICs. In addition, recent mutant COVID-19 outbreaks may counteract advances in epidemic control and economic recovery in HICs. To explore the consequences of vaccine (in)equity in the face of evolving COVID-19 strains, we examine vaccine allocation strategies using a multistrain metapopulation model. Our results show that vaccine inequity provides only limited and short-term benefits to HICs. Sharper disparities in vaccine allocation between HICs and LMICs lead to earlier and larger outbreaks of new waves. Equitable vaccine allocation strategies, in contrast, substantially curb the spread of new strains. For HICs, making immediate and generous vaccine donations to LMICs is a practical pathway to protect everyone.

Dynamic Analysis and Optimal Control of a Multi-Strain Coinfection Model with Amplification and Vaccination

Dynamic Analysis and Optimal Control of a Multi-Strain Coinfection Model with Amplification and Vaccination

Estimating the Impact of Low Influenza Activity in 2020 on Population Immunity and Future Influenza Seasons in the United States.

BackgroundInfluenza activity in the 2020–2021 season was remarkably low, likely due to implementation of public health preventive measures such as social distancing, mask wearing, and school closure. With waning immunity, the impact of low influenza activity in the 2020–2021 season on the following season is unknown.MethodsWe built a multistrain compartmental model that captures immunity over multiple influenza seasons in the United States. Compared with the counterfactual case, where influenza activity remained at the normal level in 2020–2021, we estimated the change in the number of hospitalizations when the transmission rate was decreased by 20% in 2020–2021. We varied the level of vaccine uptake and effectiveness in 2021–2022. We measured the change in population immunity over time by varying the number of seasons with lowered influenza activity.ResultsWith the lowered influenza activity in 2020–2021, the model estimated 102 000 (95% CI, 57 000–152 000) additional hospitalizations in 2021–2022, without changes in vaccine uptake and effectiveness. The estimated changes in hospitalizations varied depending on the level of vaccine uptake and effectiveness in the following year. Achieving a 50% increase in vaccine coverage was necessary to avert the expected increase in hospitalization in the next influenza season. If the low influenza activity were to continue over several seasons, population immunity would remain low during those seasons, with 48% of the population susceptible to influenza infection.ConclusionsOur study projected a large compensatory influenza season in 2021–2022 due to a light season in 2020–2021. However, higher influenza vaccine uptake would reduce this projected increase in influenza.

Control Strategies for a Multi-strain Epidemic Model.

This article studies a multi-strain epidemic model with diffusion and environmental heterogeneity. We address the question of a control strategy for multiple strains of the infectious disease by investigating how the local distributions of the transmission and recovery rates affect the dynamics of the disease. Our study covers both full model (in which case the diffusion rates for all subgroups of the population are positive) and the ODE–PDE case (in which case we require a total lock-down of the susceptible subgroup and allow the infected subgroups to have positive diffusion rates). In each case, a basic reproduction number of the epidemic model is defined and it is shown that if this reproduction number is less than one then the disease will be eradicated in the long run. On the other hand, if the reproduction number is greater than one, then the disease will become permanent. Moreover, we show that when the disease is permanent, creating a common safety area against all strains and lowering the diffusion rate of the susceptible subgroup will result in reducing the number of infected populations. Numerical simulations are presented to support our theoretical findings.

Harnessing natural variation to identify cis regulators of sex-biased gene expression in a multi-strain mouse liver model.

Sex differences in gene expression are widespread in the liver, where many autosomal factors act in tandem with growth hormone signaling to regulate individual variability of sex differences in liver metabolism and disease. Here, we compare hepatic transcriptomic and epigenetic profiles of mouse strains C57BL/6J and CAST/EiJ, representing two subspecies separated by 0.5-1 million years of evolution, to elucidate the actions of genetic factors regulating liver sex differences. We identify 144 protein coding genes and 78 lncRNAs showing strain-conserved sex bias; many have gene ontologies relevant to liver function, are more highly liver-specific and show greater sex bias, and are more proximally regulated than genes whose sex bias is strain-dependent. The strain-conserved genes include key growth hormone-dependent transcriptional regulators of liver sex bias; however, three other transcription factors, Trim24, Tox, and Zfp809, lose their sex-biased expression in CAST/EiJ mouse liver. To elucidate the observed strain specificities in expression, we characterized the strain-dependence of sex-biased chromatin opening and enhancer marks at cis regulatory elements (CREs) within expression quantitative trait loci (eQTL) regulating liver sex-biased genes. Strikingly, 208 of 286 eQTLs with strain-specific, sex-differential effects on expression were associated with a complete gain, loss, or reversal of the sex differences in expression between strains. Moreover, 166 of the 286 eQTLs were linked to the strain-dependent gain or loss of localized sex-biased CREs. Remarkably, a subset of these CREs apparently lacked strain-specific genetic variants yet showed coordinated, strain-dependent sex-biased epigenetic regulation. Thus, we directly link hundreds of strain-specific genetic variants to the high variability in CRE activity and expression of sex-biased genes and uncover underlying genetically-determined epigenetic states controlling liver sex bias in genetically diverse mouse populations.

Complex dynamics of multi strain TB model under nonlocal and nonsingular fractal fractional operator

Researchers have recently begun to use fractal fractional operators in the Atangana–Baleanu sense to analyze complicated dynamics of various models in applied sciences, as the Atangana–Baleanu operator generalizes the integer and fractional order operators. To analyze the complex dynamics of the multi-strain TB model, we use the AB-fractal fractional operator. We use the Banach fixed point theorem to ensure that at most one solution exists to the model. Further, the Ulam–Hyers type stability of the model is investigated with the help of functional analysis. The Adams–Bashforth approach is used to get numerical results for the proposed model. The analysis of the chaotic behavior of the proposed TB model was missing in the literature. Therefore, for different values of fractional and fractal order, we study the nonlinear dynamics and chaotic behavior of the obtained results of the proposed model.

A brief note on a multistrain SIR model with complete cross-protection and nonlinear force of infection

We formulate and investigate a compartmental model for a multi-strain SIR disease with complete cross immunity and nonlinear force of infection. More specifically we consider a hyperbolic force of infection with saturation effects. Using a combination of analytical and computational methods, we find that under such a nonlinear force of infection in the longterm several strains can be established in a population. This is in contrast to a comparable model with SI mass action transmission, i.e., the more familiar linear force of infection, in which case a principle of competitive exclusion holds, such that only the strain with the highest basic reproduction number will be present in the longterm.

Mathematical analysis of multi-target cells and multi-strain age-structured model with two HIV infection routes

In this paper, we propose detailed and reasonable viral dynamics by using a multi-compartment model that incorporating the age since the infection of multiple infected cells, multiple target cells (Langerhans-cells and CD4[Formula: see text] T-cells), multiple viral strains (CCR5 and CXR4 HIV) and multiple infection routes (cell-to-cell and cell-to-virus). The basic reproduction number, [Formula: see text], of the whole model is derived from two transmission mechanisms: one is the potential trigger from the infection routes for a single target cell and other is the joint effect of multiple viral infections for multi-target cells. Accordingly, we study the global stability of the steady states for the single target model. For the whole model, we prove that the infection-free steady state is globally asymptotically stable if [Formula: see text], whereas viruses persist uniformly if [Formula: see text]. Numerical simulations are carried out to illustrate the theoretical results. Sensitive analyses expound the effect of model parameters on the comprehensive reproduction number. It is remarkable to find that simultaneous control of HIV infection for two target cells can effectively reduce the viral loads within-host. Finally, our work suggests that the synergetic mechanism of multi-target cells and multi-strain cannot be ignored during treatment.

The local stability of a modified multi-strain SIR model for emerging viral strains.

We study a novel multi-strain SIR epidemic model with selective immunity by vaccination. A newer strain is made to emerge in the population when a preexisting strain has reached equilbrium. We assume that this newer strain does not exhibit cross-immunity with the original strain, hence those who are vaccinated and recovered from the original strain become susceptible to the newer strain. Recent events involving the COVID-19 virus shows that it is possible for a viral strain to emerge from a population at a time when the influenza virus, a well-known virus with a vaccine readily available, is active in a population. We solved for four different equilibrium points and investigated the conditions for existence and local stability. The reproduction number was also determined for the epidemiological model and found to be consistent with the local stability condition for the disease-free equilibrium.

Near-optimal control for a stochastic multi-strain epidemic model with age structure and Markovian switching

ABSTRACT Stochastic noise can affect the dynamics of infectious diseases. In this paper, a new stochastic multi-strain epidemic model with white noise, Markovian switching, vaccination control and age structure is established. Some priori estimates of the susceptible, infected and recovered are obtained. Under the condition of the objective function is minimised, we formulate sufficient and necessary conditions for the near-optimal control problems of the system, which is using a nearly maximum condition of the Hamiltonian function. The great influence of age structure, white noise, Markovian switching and vaccination control on the dynamical behaviour of infectious diseases and the existence of near-optimal control are demonstrated by numerical simulations.

Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic.

This paper investigates the global stability analysis of two-strain epidemic model with two general incidence rates. The problem is modelled by a system of six nonlinear ordinary differential equations describing the evolution of susceptible, exposed, infected and removed individuals. The wellposedness of the suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points are given, namely the disease-free equilibrium, the endemic equilibrium with respect to strain 1, the endemic equilibrium with respect to strain 2, and the last endemic equilibrium with respect to both strains. By constructing suitable Lyapunov functional, the global stability of the disease-free equilibrium is proved depending on the basic reproduction number R_0. Furthermore, using other appropriate Lyapunov functionals, the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number R^{1}_0 and the strain 2 reproduction number R^{2}_0. Numerical simulations are performed in order to confirm the different theoretical results. It was observed that the model with a generalized incidence functions encompasses a large number of models with classical incidence functions and it gives a significant wide view about the equilibria stability. Numerical comparison between the model results and COVID-19 clinical data was conducted. Good fit of the model to the real clinical data was remarked. The impact of the quarantine strategy on controlling the infection spread is discussed. The generalization of the problem to a more complex compartmental model is illustrated at the end of this paper.

Dynamical analysis for delayed virus infection models with cell-to-cell transmission and density-dependent diffusion

In this paper, certain delayed virus dynamical models with cell-to-cell infection and density-dependent diffusion are investigated. For the viral model with a single strain, we have proved the well-posedness and studied the global stabilities of equilibria by defining the basic reproductive number [Formula: see text] and structuring proper Lyapunov functional. Moreover, we found that the infection-free equilibrium is globally asymptotically stable if [Formula: see text], and the infection equilibrium is globally asymptotically stable if [Formula: see text]. For the multi-strain model, we found that all viral strains coexist if the corresponding basic reproductive number [Formula: see text], while virus will extinct if [Formula: see text]. As a result, we found that delay and the density-dependent diffusion does not influence the global stability of the model with cell-to-cell infection and homogeneous Neumann boundary conditions.

Analysis and Optimal Control of a Multistrain SEIR Epidemic Model with Saturated Incidence Rate and Treatment

In this paper, we study the dynamic of a multi-strain SEIR model with both saturated incidence and treatment functions. Two basic reproduction numbers are extracted from the epidemic model, noted $$R_{0,1}$$ and $$R_{0,2}$$ . Using the Lyapunov method, we investigate the global stability of the disease free equilibrium and prove that it is globally asymptotically stable when $$R_{0,1}$$ and $$R_{0,2}$$ are less than one. Moreover, we formulate the optimal control problem, solve it, and perform some numerical simulations, to support the analytical results and test how well the proposed model may be applied in practice.

Global stability of a multistrain SIS model with superinfection and patch structure

We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al. [Nonlinear Anal Real World Appl. 2006;7:235–247], we show that these parameters completely determine the global dynamics of the system: for any number of patches and strains with different infectivities, any subset of the strains can stably coexist depending on the particular choice of the parameters.

Threshold Dynamics and Competitive Exclusion in a Virus Infection Model with General Incidence Function and Density-Dependent Diffusion

In this paper, we investigate single-strain and multistrain viral infection models with general incidence function and density-dependent diffusion subject to the homogeneous Neumann boundary conditions. For the single-strain viral infection model, by using the linearization method and constructing appropriate Lyapunov functionals, we obtain that the global threshold dynamics of the model is determined by the reproductive numbers for viral infection ℛ0. For the multistrain viral infection model, we have discussed the competitive exclusion problem. If the reproduction number ℛi for strain i is maximal and larger than one, the steady state Ei corresponding to the strain i is globally stable. Thus, competitive exclusion happens and all other strains die out except strain i. Meanwhile, we can prove that the single-strain and multistrain viral infection models are well posed. Furthermore, numerical simulations are also carried out to illustrate the theoretical results, which is seldom seen in the relevant known literatures.