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  1. Article ; Online: Optimal Control applied to a SEIR model of 2019-nCoV with social distancing

    Mallela, Abhishek

    Abstract: Does the implementation of social distancing measures have merit in controlling the spread of the novel coronavirus? In this study, we develop a mathematical model to explore the effect of social distancing on new disease infections. Mathematical ... ...

    Abstract Does the implementation of social distancing measures have merit in controlling the spread of the novel coronavirus? In this study, we develop a mathematical model to explore the effect of social distancing on new disease infections. Mathematical analyses of our model indicate that successful eradication of the disease is strongly dependent on the chosen preventive measure. Numerical computations of the model solution demonstrate that the ability to flatten the curve becomes easier as social distancing is strictly enforced. Based on our model, we also formulate an optimal control problem and solve it using Pontryagin's Maximum Principle and an efficient numerical iterative method. Our numerical results of an optimal 2019-nCoV treatment protocol that yields a minimum disease burden from this disease indicates that social distancing is vitally important.
    Keywords covid19
    Publisher MedRxiv; WHO
    Document type Article ; Online
    DOI 10.1101/2020.04.10.20061069
    Database COVID19

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  2. Article ; Online: Optimal Control applied to a SEIR model of 2019-nCoV with social distancing

    Mallela, Abhishek

    medRxiv

    Abstract: Does the implementation of social distancing measures have merit in controlling the spread of the novel coronavirus? In this study, we develop a mathematical model to explore the effect of social distancing on new disease infections. Mathematical ... ...

    Abstract Does the implementation of social distancing measures have merit in controlling the spread of the novel coronavirus? In this study, we develop a mathematical model to explore the effect of social distancing on new disease infections. Mathematical analyses of our model indicate that successful eradication of the disease is strongly dependent on the chosen preventive measure. Numerical computations of the model solution demonstrate that the ability to flatten the curve becomes easier as social distancing is strictly enforced. Based on our model, we also formulate an optimal control problem and solve it using Pontryagin9s Maximum Principle and an efficient numerical iterative method. Our numerical results of an optimal 2019-nCoV treatment protocol that yields a minimum disease burden from this disease indicates that social distancing is vitally important.
    Keywords covid19
    Language English
    Publishing date 2020-04-14
    Publisher Cold Spring Harbor Laboratory Press
    Document type Article ; Online
    DOI 10.1101/2020.04.10.20061069
    Database COVID19

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  3. Article ; Online: Optimal management of stochastic invasion in a metapopulation with Allee effects.

    Mallela, Abhishek / Hastings, Alan

    Journal of theoretical biology

    2022  Volume 549, Page(s) 111221

    Abstract: Invasive species account for incalculable damages worldwide, in both ecological and bioeconomic terms. The question of how a network of invasive populations can be optimally managed is one that deserves further exploration. A study accounting for partial ...

    Abstract Invasive species account for incalculable damages worldwide, in both ecological and bioeconomic terms. The question of how a network of invasive populations can be optimally managed is one that deserves further exploration. A study accounting for partial observability and imperfect detection, in particular, could yield useful insights into species eradication efforts. Here, we generalized a simple model system that we developed in previous work. This model consists of three interacting populations with underlying strong Allee effects and stochastic dynamics, inhabiting distinct locations connected by dispersal, which can generate bistability. To explore the stochastic dynamics, we formulated an individual-based modeling approach. Next, using the theory of continuous-time Markov chains, we approximated the original high-dimensional model by a Markov chain with eight states, with each state corresponding to a combination of population thresholds. We then used the reduced model as the core for a powerful decision-making tool, referred to as a Partially Observable Markov Decision Process (POMDP). Analysis of this POMDP indicates when the system results in optimal management outcomes.
    MeSH term(s) Markov Chains ; Models, Biological ; Population Dynamics ; Stochastic Processes
    Language English
    Publishing date 2022-07-16
    Publishing country England
    Document type Journal Article
    ZDB-ID 2972-5
    ISSN 1095-8541 ; 0022-5193
    ISSN (online) 1095-8541
    ISSN 0022-5193
    DOI 10.1016/j.jtbi.2022.111221
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  4. Article ; Online: Differential contagiousness of respiratory disease across the United States.

    Mallela, Abhishek / Lin, Yen Ting / Hlavacek, William S

    Epidemics

    2023  Volume 45, Page(s) 100718

    Abstract: The initial contagiousness of a communicable disease within a given population is quantified by the basic reproduction number, ... ...

    Abstract The initial contagiousness of a communicable disease within a given population is quantified by the basic reproduction number, R
    MeSH term(s) Humans ; United States/epidemiology ; Bayes Theorem ; COVID-19/epidemiology ; Basic Reproduction Number
    Language English
    Publishing date 2023-09-22
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 2467993-8
    ISSN 1878-0067 ; 1755-4365
    ISSN (online) 1878-0067
    ISSN 1755-4365
    DOI 10.1016/j.epidem.2023.100718
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  5. Article ; Online: The Role of Stochasticity in Noise-Induced Tipping Point Cascades: A Master Equation Approach.

    Mallela, Abhishek / Hastings, Alan

    Bulletin of mathematical biology

    2021  Volume 83, Issue 5, Page(s) 53

    Abstract: Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less explored and is an important one. A study of noise- ... ...

    Abstract Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less explored and is an important one. A study of noise-induced tipping, in particular, could provide key insights into tipping cascades. Here, we consider a specific example of a simple model system that could have cascading tipping points. This model consists of two interacting populations with underlying Allee effects and stochastic dynamics, in separate patches connected by dispersal, which can generate bistability. From an ecological standpoint, we look for rescue effects whereby one population can prevent the collapse of a second population. As a way to investigate the stochastic dynamics, we use an individual-based modeling approach rooted in chemical reaction network theory. Then, using continuous-time Markov chains and the theory of first passage times, we essentially approximate, or emulate, the original high-dimensional model by a Markov chain with just three states, where each state corresponds to a combination of population thresholds. Analysis of this reduced model shows when the system is likely to recover, as well as when tipping cascades through the whole system.
    MeSH term(s) Animals ; Ecology/methods ; Markov Chains ; Models, Biological ; Population Dynamics
    Language English
    Publishing date 2021-03-31
    Publishing country United States
    Document type Journal Article
    ZDB-ID 184905-0
    ISSN 1522-9602 ; 0007-4985 ; 0092-8240
    ISSN (online) 1522-9602
    ISSN 0007-4985 ; 0092-8240
    DOI 10.1007/s11538-021-00889-1
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  6. Article ; Online: Tipping Cascades in a Multi-patch System with Noise and Spatial Coupling.

    Mallela, Abhishek / Hastings, Alan

    Bulletin of mathematical biology

    2021  Volume 83, Issue 11, Page(s) 112

    Abstract: Forecasting tipping points in spatially extended systems is a key area of interest to ecologists. A slowly declining spatially distributed population is an important example of an ecological system that could exhibit a cascade of tipping points. Here, we ...

    Abstract Forecasting tipping points in spatially extended systems is a key area of interest to ecologists. A slowly declining spatially distributed population is an important example of an ecological system that could exhibit a cascade of tipping points. Here, we develop a spatial two-patch model with environmental stochasticity that is slowly forced through population collapse, in the presence of changing environmental conditions. We begin with a basic spatial model, then introduce a fast-slow version of the model using geometric singular perturbation theory, followed by the inclusion of stochasticity. Using the spectral density of the fluctuating subpopulation in each patch, we derive analytic expressions for candidate indicators of population extinction and evaluate their performance through a simulation study. We find that coupling and spatial heterogeneity decrease the magnitude of the proposed indicators in coupled populations relative to isolated populations. Moreover, the degree of coupling dictates the trends in summary statistics. We conclude that this theory may be applied to other contexts, including the control of invasive species.
    MeSH term(s) Computer Simulation ; Ecosystem ; Mathematical Concepts ; Models, Biological ; Population Dynamics
    Language English
    Publishing date 2021-09-30
    Publishing country United States
    Document type Journal Article ; Research Support, U.S. Gov't, Non-P.H.S.
    ZDB-ID 184905-0
    ISSN 1522-9602 ; 0007-4985 ; 0092-8240
    ISSN (online) 1522-9602
    ISSN 0007-4985 ; 0092-8240
    DOI 10.1007/s11538-021-00943-y
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  7. Article ; Online: Differential contagiousness of respiratory disease across the United States

    Mallela, Abhishek / Lin, Yen Ting / Hlavacek, William S

    medRxiv

    Abstract: The initial contagiousness of a communicable disease within a given population is quantified by the basic reproduction number, denoted R_0. The value of R_0 gives the expected number of new cases generated by an infectious person in a wholly susceptible ... ...

    Abstract The initial contagiousness of a communicable disease within a given population is quantified by the basic reproduction number, denoted R_0. The value of R_0 gives the expected number of new cases generated by an infectious person in a wholly susceptible population and depends on both pathogen and population properties. On the basis of compartmental models that reproduce Coronavirus Disease 2019 (COVID-19) surveillance data, we estimated region-specific R_0 values for 280 of 384 metropolitan statistical areas (MSAs) in the United States (US), which account for 95% of the US population living in urban areas and 82% of the total population. Our estimates range from 1.9 to 7.7 and quantify the relative susceptibilities of regional populations to spread of respiratory diseases.
    Keywords covid19
    Language English
    Publishing date 2022-09-17
    Publisher Cold Spring Harbor Laboratory Press
    Document type Article ; Online
    DOI 10.1101/2022.09.15.22279948
    Database COVID19

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  8. Book ; Online: The Role of Stochasticity in Noise-Induced Tipping Point Cascades

    Mallela, Abhishek / Hastings, Alan

    A Master Equation Approach

    2020  

    Abstract: Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less well studied and is an important one. A study of noise- ...

    Abstract Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less well studied and is an important one. A study of noise-induced tipping, in particular, could provide key insights into tipping cascades. Here, we consider a specific example of a simple model system that could have cascading tipping points. This model consists of two interacting populations with underlying Allee effects and stochastic dynamics, in separate patches connected by dispersal, which can generate bistability. From an ecological standpoint, we look for rescue effects whereby one population can prevent the collapse of a second population. As a way to investigate the stochastic dynamics, we use an individual-based modeling approach rooted in chemical reaction network theory. Then, using continuous-time Markov chains and the theory of first passage times, we essentially approximate, or emulate, the original high-dimensional model by a Markov chain with just four states, where each state corresponds to a combination of population thresholds. Analysis of this reduced model shows when the system is likely to recover, as well as when tipping cascades through the whole system.

    Comment: 18 pages, 5 figures
    Keywords Mathematics - Dynamical Systems ; Quantitative Biology - Populations and Evolution ; 37N25 (Primary) ; 37N30 ; 92B99 (Secondary)
    Subject code 612
    Publishing date 2020-11-18
    Publishing country us
    Document type Book ; Online
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  9. Article ; Online: Crosstalk and ultrasensitivity in protein degradation pathways.

    Mallela, Abhishek / Nariya, Maulik K / Deeds, Eric J

    PLoS computational biology

    2020  Volume 16, Issue 12, Page(s) e1008492

    Abstract: Protein turnover is vital to cellular homeostasis. Many proteins are degraded efficiently only after they have been post-translationally "tagged" with a polyubiquitin chain. Ubiquitylation is a form of Post-Translational Modification (PTM): addition of a ...

    Abstract Protein turnover is vital to cellular homeostasis. Many proteins are degraded efficiently only after they have been post-translationally "tagged" with a polyubiquitin chain. Ubiquitylation is a form of Post-Translational Modification (PTM): addition of a ubiquitin to the chain is catalyzed by E3 ligases, and removal of ubiquitin is catalyzed by a De-UBiquitylating enzyme (DUB). Nearly four decades ago, Goldbeter and Koshland discovered that reversible PTM cycles function like on-off switches when the substrates are at saturating concentrations. Although this finding has had profound implications for the understanding of switch-like behavior in biochemical networks, the general behavior of PTM cycles subject to synthesis and degradation has not been studied. Using a mathematical modeling approach, we found that simply introducing protein turnover to a standard modification cycle has profound effects, including significantly reducing the switch-like nature of the response. Our findings suggest that many classic results on PTM cycles may not hold in vivo where protein turnover is ubiquitous. We also found that proteins sharing an E3 ligase can have closely related changes in their expression levels. These results imply that it may be difficult to interpret experimental results obtained from either overexpressing or knocking down protein levels, since changes in protein expression can be coupled via E3 ligase crosstalk. Understanding crosstalk and competition for E3 ligases will be key in ultimately developing a global picture of protein homeostasis.
    MeSH term(s) Catalysis ; Humans ; Protein Processing, Post-Translational ; Proteins/chemistry ; Proteolysis ; Ubiquitin-Protein Ligases/metabolism
    Chemical Substances Proteins ; Ubiquitin-Protein Ligases (EC 2.3.2.27)
    Language English
    Publishing date 2020-12-28
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2193340-6
    ISSN 1553-7358 ; 1553-734X
    ISSN (online) 1553-7358
    ISSN 1553-734X
    DOI 10.1371/journal.pcbi.1008492
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  10. Article ; Online: Robustness and the evolution of length control strategies in the T3SS and flagellar hook.

    Nariya, Maulik K / Mallela, Abhishek / Shi, Jack J / Deeds, Eric J

    Biophysical journal

    2021  Volume 120, Issue 17, Page(s) 3820–3830

    Abstract: Bacterial cells construct many structures, such as the flagellar hook and the type III secretion system (T3SS) injectisome, that aid in crucial physiological processes such as locomotion and pathogenesis. Both of these structures involve long ... ...

    Abstract Bacterial cells construct many structures, such as the flagellar hook and the type III secretion system (T3SS) injectisome, that aid in crucial physiological processes such as locomotion and pathogenesis. Both of these structures involve long extracellular channels, and the length of these channels must be highly regulated in order for these structures to perform their intended functions. There are two leading models for how length control is achieved in the flagellar hook and T3SS needle: the substrate switching model, in which the length is controlled by assembly of an inner rod, and the ruler model, in which a molecular ruler controls the length. Although there is qualitative experimental evidence to support both models, comparatively little has been done to quantitatively characterize these mechanisms or make detailed predictions that could be used to unambiguously test these mechanisms experimentally. In this work, we constructed a mathematical model of length control based on the ruler mechanism and found that the predictions of this model are consistent with experimental data-not just for the scaling of the average length with the ruler protein length, but also for the variance. Interestingly, we found that the ruler mechanism allows for the evolution of needles with large average lengths without the concomitant large increase in variance that occurs in the substrate switching mechanism. In addition to making further predictions that can be tested experimentally, these findings shed new light on the trade-offs that may have led to the evolution of different length control mechanisms in different bacterial species.
    MeSH term(s) Bacterial Proteins/genetics ; Flagella ; Type III Secretion Systems
    Chemical Substances Bacterial Proteins ; Type III Secretion Systems
    Language English
    Publishing date 2021-07-09
    Publishing country United States
    Document type Journal Article
    ZDB-ID 218078-9
    ISSN 1542-0086 ; 0006-3495
    ISSN (online) 1542-0086
    ISSN 0006-3495
    DOI 10.1016/j.bpj.2021.05.032
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