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Haun A, Fain B, Dobrovolny HM. Effect of cellular regeneration and viral transmission mode on viral spread. J Theor Biol 2023; 558:111370. [PMID: 36460057 DOI: 10.1016/j.jtbi.2022.111370] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2022] [Revised: 11/03/2022] [Accepted: 11/18/2022] [Indexed: 12/03/2022]
Abstract
Illness negatively affects all aspects of life and one major cause of illness is viral infections. Some viral infections can last for weeks; others, like influenza (the flu), can resolve quickly. During infections, uninfected cells can replicate in order to replenish the cells that have died due to the virus. Many viral models, especially those for short-lived infections like influenza, tend to ignore cellular regeneration since many think that uncomplicated influenza resolves much faster than cells regenerate. This research accounts for cellular regeneration, using an agent-based framework, and varies the regeneration rate in order to understand how cell regeneration affects viral infection dynamics under assumptions of different modes of transmission. We find that although the general trends in peak viral load, time of viral peak, and chronic viral load as regeneration rate changes are the same for cell-free or cell-to-cell transmission, the changes are more extreme for cell-to-cell transmission due to limited access of infected cells to newly generated cells.
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Affiliation(s)
- Asher Haun
- Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX, United States of America
| | - Baylor Fain
- Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX, United States of America
| | - Hana M Dobrovolny
- Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX, United States of America.
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Ndjomatchoua FT, Djomo TLM, Kemwoue FF, Gninzanlong CL, Kepnang MP, Siewe MS, Tchawoua C, Pedro SA, Kofane TC. Amplitude response, Melnikov's criteria, and chaos occurrence in a Duffing's system subjected to an external periodic excitation with a variable shape. CHAOS (WOODBURY, N.Y.) 2022; 32:083144. [PMID: 36049915 DOI: 10.1063/5.0082235] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 07/28/2022] [Indexed: 06/15/2023]
Abstract
The present study considers the nonlinear dynamics of a Duffing oscillator under a symmetric potential subjected to a pulse-type excitation with a deformable shape. Our attention is focused on the effects of the external excitation shape parameter r and its period. The frequency response of the system is derived by using a semi-analytical approach. Interestingly, the frequency-response curve displays a large number of resonance peaks and anti-resonance peaks as well. Surprisingly, a resonance phenomenon termed here as shape-induced-resonance is noticed as it occurs solely due to the change in the shape parameter of the external periodic force. The system exhibits amplitude jumps and hysteresis depending on r. The critical driving magnitude for the chaos occurrence is investigated through Melnikov's method. Numerical analysis based on bifurcation diagrams and Lyapunov exponent is used to show how chaos occurs in the system. It is shown that the threshold amplitude of the excitation to observe chaotic dynamics decreases/increases for small/large values of r. In general, the theoretical estimates match with numerical simulations and electronic simulations as well.
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Affiliation(s)
- Frank T Ndjomatchoua
- Spatial Transformation of Landscapes, Sustainable Impact through Rice-Based Systems, International Rice Research Institute (IRRI), DAPO Box 7777-1301, Metro Manila, Philippines
| | - Thierry L M Djomo
- Department of Civil Engineering, National Higher Polytechnic Institute, University of Bamenda, P.O. BOX 39, Bambili, Bamenda, Cameroon
| | - Florent F Kemwoue
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon
| | - Carlos L Gninzanlong
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon
| | - Maxime P Kepnang
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon
| | - Martin S Siewe
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon
| | - Clément Tchawoua
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon
| | - Sansao A Pedro
- Departamento de Matemática e Informatica, Faculdade de Ciências, Universidade Eduardo Mondlane, 254 Maputo, Mozambique
| | - Timoleon C Kofane
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon
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Treatment of Respiratory Viral Coinfections. EPIDEMIOLGIA (BASEL, SWITZERLAND) 2022; 3:81-96. [PMID: 36417269 PMCID: PMC9620919 DOI: 10.3390/epidemiologia3010008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Revised: 01/18/2022] [Accepted: 02/01/2022] [Indexed: 12/14/2022]
Abstract
With the advent of rapid multiplex PCR, physicians have been able to test for multiple viral pathogens when a patient presents with influenza-like illness. This has led to the discovery that many respiratory infections are caused by more than one virus. Antiviral treatment of viral coinfections can be complex because treatment of one virus will affect the time course of the other virus. Since effective antivirals are only available for some respiratory viruses, careful consideration needs to be given on the effect treating one virus will have on the dynamics of the other virus, which might not have available antiviral treatment. In this study, we use mathematical models of viral coinfections to assess the effect of antiviral treatment on coinfections. We examine the effect of the mechanism of action, relative growth rates of the viruses, and the assumptions underlying the interaction of the viruses. We find that high antiviral efficacy is needed to suppress both infections. If high doses of both antivirals are not achieved, then we run the risk of lengthening the duration of coinfection or even of allowing a suppressed virus to replicate to higher viral titers.
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Pinky L, Gonzalez-Parra G, Dobrovolny HM. Effect of stochasticity on coinfection dynamics of respiratory viruses. BMC Bioinformatics 2019; 20:191. [PMID: 30991939 PMCID: PMC6469119 DOI: 10.1186/s12859-019-2793-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2018] [Accepted: 04/03/2019] [Indexed: 12/17/2022] Open
Abstract
Background Respiratory viral infections are a leading cause of mortality worldwide. As many as 40% of patients hospitalized with influenza-like illness are reported to be infected with more than one type of virus. However, it is not clear whether these infections are more severe than single viral infections. Mathematical models can be used to help us understand the dynamics of respiratory viral coinfections and their impact on the severity of the illness. Most models of viral infections use ordinary differential equations (ODE) that reproduce the average behavior of the infection, however, they might be inaccurate in predicting certain events because of the stochastic nature of viral replication cycle. Stochastic simulations of single virus infections have shown that there is an extinction probability that depends on the size of the initial viral inoculum and parameters that describe virus-cell interactions. Thus the coinfection dynamics predicted by the ODE might be difficult to observe in reality. Results In this work, a continuous-time Markov chain (CTMC) model is formulated to investigate probabilistic outcomes of coinfections. This CTMC model is based on our previous coinfection model, expressed in terms of a system of ordinary differential equations. Using the Gillespie method for stochastic simulation, we examine whether stochastic effects early in the infection can alter which virus dominates the infection. Conclusions We derive extinction probabilities for each virus individually as well as for the infection as a whole. We find that unlike the prediction of the ODE model, for similar initial growth rates stochasticity allows for a slower growing virus to out-compete a faster growing virus. Electronic supplementary material The online version of this article (10.1186/s12859-019-2793-6) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Lubna Pinky
- Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX, USA.,Department of Pediatrics, University of Tennessee Health Science Center, Memphis, TN, USA
| | | | - Hana M Dobrovolny
- Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX, USA.
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Handel A, Liao LE, Beauchemin CA. Progress and trends in mathematical modelling of influenza A virus infections. ACTA ACUST UNITED AC 2018. [DOI: 10.1016/j.coisb.2018.08.009] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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Melville K, Rodriguez T, Dobrovolny HM. Investigating Different Mechanisms of Action in Combination Therapy for Influenza. Front Pharmacol 2018; 9:1207. [PMID: 30405419 PMCID: PMC6206389 DOI: 10.3389/fphar.2018.01207] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Accepted: 10/03/2018] [Indexed: 01/15/2023] Open
Abstract
Combination therapy for influenza can have several benefits, from reducing the emergence of drug resistant virus strains to decreasing the cost of antivirals. However, there are currently only two classes of antivirals approved for use against influenza, limiting the possible combinations that can be considered for treatment. However, new antivirals are being developed that target different parts of the viral replication cycle, and their potential for use in combination therapy should be considered. The role of antiviral mechanism of action in the effectiveness of combination therapy has not yet been systematically investigated to determine whether certain antiviral mechanisms of action pair well in combination. Here, we use a mathematical model of influenza to model combination treatment with antivirals having different mechanisms of action to measure peak viral load, infection duration, and synergy of different drug combinations. We find that antivirals that lower the infection rate and antivirals that increase the duration of the eclipse phase perform poorly in combination with other antivirals.
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Affiliation(s)
- Kelli Melville
- Physics Department, East Carolina University, Greenville, NC, United States
| | - Thalia Rodriguez
- Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX, United States
| | - Hana M. Dobrovolny
- Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX, United States
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