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

ABSTRACT: 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.

SUBMITTER: Fudolig M

PROVIDER: S-EPMC7725381 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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

Fudolig Miguel M Howard Reka R

PloS one 20201209 12

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 popu ...[more]

PMID: 33296417

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Project description:Isolations of sylvatic dengue-2 virus from mosquitoes, humans and non-human primates in Senegal show synchronized multi-annual dynamics over the past 50 years. Host demography has been shown to directly affect the period between epidemics in other pathogen systems, therefore, one might expect unsynchronized multi-annual cycles occurring in hosts with dramatically different birth rates and life spans. However, in Senegal, we observe a single synchronized eight-year cycle across all vector species, suggesting synchronized dynamics in all vertebrate hosts. In the current study, we aim to explore two specific hypotheses: 1) primates with different demographics will experience outbreaks of dengue at different periodicities when observed as isolated systems, and that coupling of these subsystems through mosquito biting will act to synchronize incidence; and 2) the eight-year periodicity of isolations observed across multiple primate species is the result of long-term cycling in population immunity in the host populations. To test these hypotheses, we develop a multi-host, multi-vector Susceptible, Infected, Removed (SIR) model to explore the effects of coupling multiple host-vector systems of dengue virus transmission through cross-species biting rates. We find that under small amounts of coupling, incidence in the host species synchronize. Long-period multi-annual dynamics are observed only when prevalence in troughs reaches vanishingly small levels (< 10(-10)), suggesting that these dynamics are inconsistent with sustained transmission in this setting, but are consistent with local dengue virus extinctions followed by reintroductions. Inclusion of a constant introduction of infectious individuals into the system causes the multi-annual periods to shrink, while the effects of coupling remain the same. Inclusion of a stochastic rate of introduction allows for multi-annual periods at a cost of reduced synchrony. Thus, we conclude that the eight-year period separating amplifications of dengue may be explained by cycling in immunity with stochastic introductions.

Project description:BackgroundThe new Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2), which was first detected in Wuhan (China) in December of 2019 is responsible for the current global pandemic. Phylogenetic analysis revealed that it is similar to other betacoronaviruses, such as SARS-CoV and Middle-Eastern Respiratory Syndrome, MERS-CoV. Its genome is ∼ 30 kb in length and contains two large overlapping polyproteins, ORF1a and ORF1ab that encode for several structural and non-structural proteins. The non-structural protein 1 (nsp1) is arguably the most important pathogenic determinant, and previous studies on SARS-CoV indicate that it is both involved in viral replication and hampering the innate immune system response. Detailed experiments of site-specific mutagenesis and in vitro reconstitution studies determined that the mechanisms of action are mediated by (a) the presence of specific amino acid residues of nsp1 and (b) the interaction between the protein and the host's small ribosomal unit. In fact, substitution of certain amino acids resulted in reduction of its negative effects.MethodsA total of 17,928 genome sequences were obtained from the GISAID database (December 2019 to July 2020) from patients infected by SARS-CoV-2 from different areas around the world. Genomes alignment was performed using MAFFT (REFF) and the nsp1 genomic regions were identified using BioEdit and verified using BLAST. Nsp1 protein of SARS-CoV-2 with and without deletion have been subsequently modelled using I-TASSER.ResultsWe identified SARS-CoV-2 genome sequences, from several Countries, carrying a previously unknown deletion of 9 nucleotides in position 686-694, corresponding to the AA position 241-243 (KSF). This deletion was found in different geographical areas. Structural prediction modelling suggests an effect on the C-terminal tail structure.ConclusionsModelling analysis of a newly identified deletion of 3 amino acids (KSF) of SARS-CoV-2 nsp1 suggests that this deletion could affect the structure of the C-terminal region of the protein, important for regulation of viral replication and negative effect on host's gene expression. In addition, substitution of the two amino acids (KS) from nsp1 of SARS-CoV was previously reported to revert loss of interferon-alpha expression. The deletion that we describe indicates that SARS-CoV-2 is undergoing profound genomic changes. It is important to: (i) confirm the spreading of this particular viral strain, and potentially of strains with other deletions in the nsp1 protein, both in the population of asymptomatic and pauci-symptomatic subjects, and (ii) correlate these changes in nsp1 with potential decreased viral pathogenicity.

Dataset Information

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

Publications

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

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