Competitive exclusion in a vector-host epidemic model with distributed delay(†)

Revisiting the exclusion principle in epidemiology at the limit of a large competitive advantage

The competitive exclusion principle in epidemiology implies that when competing strains of a pathogen provide complete protection for each other, the strain with the largest reproduction number outcompetes the other strains and drives them to extinction. The introduction of various trade-off mechanisms may facilitate the coexistence of competing strains, especially when their respective basic reproduction numbers are close so that the competition between the strains is weak. Yet, one may expect that a substantial competitive advantage of one of the strains will eventually outbalance trade-off mechanisms driving less competitive strains to extinction. The literature, however, lacks a rigorous validation of this statement. In this work, we challenge the validity of the exclusion principle at a limit in which one strain has a vast competitive advantage over the other strains. We show that when one strain is significantly more transmissible than the others, and under broad conditions, an epidemic system with two strains has a stable endemic equilibrium in which both strains coexist with comparable prevalence. Thus, the competitive exclusion principle does not unconditionally hold beyond the established case of complete immunity.

A multi-strain model with asymptomatic transmission: Application to COVID-19 in the US

COVID-19, induced by the SARS-CoV-2 infection, has caused an unprecedented pandemic in the world. New variants of the virus have emerged and dominated the virus population. In this paper, we develop a multi-strain model with asymptomatic transmission to study how the asymptomatic or pre-symptomatic infection influences the transmission between different strains and control strategies that aim to mitigate the pandemic. Both analytical and numerical results reveal that the competitive exclusion principle still holds for the model with the asymptomatic transmission. By fitting the model to the COVID-19 case and viral variant data in the US, we show that the omicron variants are more transmissible but less fatal than the previously circulating variants. The basic reproduction number for the omicron variants is estimated to be 11.15, larger than that for the previous variants. Using mask mandate as an example of non-pharmaceutical interventions, we show that implementing it before the prevalence peak can significantly lower and postpone the peak. The time of lifting the mask mandate can affect the emergence and frequency of subsequent waves. Lifting before the peak will result in an earlier and much higher subsequent wave. Caution should also be taken to lift the restriction when a large portion of the population remains susceptible. The methods and results obtained her e may be applied to the study of the dynamics of other infectious diseases with asymptomatic transmission using other control measures.

Competitive exclusion and coexistence phenomena of a two-strain SIS model on complex networks from global perspectives

Genetic heterogeneity plays an important role in exploring the interplays of microorganisms. Competitive exclusion principle is the main principle that governs causative agentries of diseases competition. Identifying coexistence mechanisms is a core issue for studying the interactions of multi-strains. In this paper, we are concerned with the dynamics of a two-strain SIS epidemic model with general incidence rate on complex networks. We derive the basic reproduction numbers and the invasion reproduction numbers associated with each strain, which determine the competitive, exclusion and coexistence of the two strains. We strictly prove that the competitive exclusion principle holds in a global sense and the endemic equilibrium coexists uniquely and globally. Numerical examples visibly illustrate the evolution of the two strains.

A general method for multiscale modelling of vector-borne disease systems

The inability to develop multiscale models which can describe vector-borne disease systems in terms of the complete pathogen life cycle which represents multiple targets for control has hindered progress in our efforts to control, eliminate and even eradicate these multi-host infections. This is because it is currently not easy to determine precisely where and how in the life cycles of vector-borne disease systems the key constrains which are regarded as crucial in regulating pathogen population dynamics in both the vertebrate host and vector host operate. In this article, we present a general method for development of multiscale models of vector-borne disease systems which integrate the within-host and between-host scales for the two hosts (a vertebrate host and a vector host) that are implicated in vector-borne disease dynamics. The general multiscale modelling method is an extension of our previous work on multiscale models of infectious disease systems which established a basic science and accompanying theory of how pathogen population dynamics at within-host scale scales up to between-host scale and in turn how it scales down from between-host scale to within-host scale. Further, the general method is applied to multiscale modelling of human onchocerciasis-a vector-borne disease system which is sometimes called river blindness as a case study.

A vector-host model to assess the impact of superinfection exclusion on vaccination strategies using dengue and yellow fever as case studies

Superinfection exclusion is a phenomenon whereby the co-infection of a host with a secondary pathogen is prevented due to a current infection by another closely-related pathogenic strain. We construct a novel vector-host mathematical model for two pathogens that exhibit superinfection exclusion and simultaneously account for vaccination strategies against them. We then derive the conditions under which an endemic disease will prevent the establishment of another through the action of superinfection exclusion and show that vaccination against the endemic strain can enable the previously suppressed strain to invade the population. Through appropriate parameterisation of the model for dengue and yellow fever we find that superinfection exclusion alone is unlikely to explain the absence of yellow fever in many regions where dengue is endemic, and that the rollout of the recently licensed dengue vaccine, Dengvaxia, is unlikely to enable the establishment of Yellow Fever in regions where it has previously been absent.

Stability and Hopf Bifurcation of a Vector-Borne Disease Model with Saturated Infection Rate and Reinfection

This paper established a delayed vector-borne disease model with saturated infection rate and cure rate. First of all, according to the basic reproductive number R ₀, we determined the disease-free equilibrium E ₀ and the endemic equilibrium E ₁. Through the analysis of the characteristic equation, we consider the stability of two equilibriums. Furthermore, the effect on the stability of the endemic equilibrium E ₁ by delay was studied, the existence of Hopf bifurcations of this system in E ₁ was analyzed, and the length of delay to preserve stability was estimated. The direction and stability of the Hopf bifurcation were also been determined. Finally, we performed some numerical simulation to illustrate our main results.

Global analysis of multi-host and multi-vector epidemic models

We formulate a multi-group and multi-vector epidemic model in which hosts' dynamics is captured by staged-progression S E I R framework and the dynamics of vectors is captured by an SI framework. The proposed model describes the evolution of a class of zoonotic infections where the pathogen is shared by m host species and transmitted by p arthropod vector species. In each host, the infectious period is structured into n stages with a corresponding infectiousness parameter to each vector species. We determine the basic reproduction number R 0 2 ( m , n , p ) and investigate the dynamics of the systems when this threshold is less or greater than one. We show that the dynamics of the multi-host, multi-stage, and multi-vector system is completely determined by the basic reproduction number and the structure of the host-vector network configuration. Particularly, we prove that the disease-free equilibrium is globally asymptotically stable (GAS) whenever R 0 2 ( m , n , p ) < 1 , and a unique strongly endemic equilibrium exists and is GAS if R 0 2 ( m , n , p ) > 1 and the host-vector configuration is irreducible. That is, either the disease dies out or persists in all hosts and all vector species.

Analysis of within-host CHIKV dynamics models with general incidence rate

In this paper we study the stability analysis of two within-host Chikungunya virus (CHIKV) dynamics models. The incidence rate between the CHIKV and the uninfected monocytes is modeled by a general nonlinear function. The second model considers two types of infected monocytes (i) latently infected monocytes which do not generate CHIKV and (ii) actively infected monocytes which produce the CHIKV particles. Sufficient conditions are found which guarantee the global stability of the positive steady states. Using the Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

Threshold dynamics of a time periodic and two--group epidemic model with distributed delay

In this paper, a time periodic and two--group reaction--diffusion epidemic model with distributed delay is proposed and investigated. We firstly introduce the basic reproduction number R0 for the model via the next generation operator method. We then establish the threshold dynamics of the model in terms of R0, that is, the disease is uniformly persistent if R0>1, while the disease goes to extinction if R0< 1. Finally, we study the global dynamics for the model in a special case when all the coefficients are independent of spatio--temporal variables.

Vector-Borne Pathogen and Host Evolution in a Structured Immuno-Epidemiological System

Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host's immune system influences the pathogen's transmission potential between hosts via vectors. Yet there are few theoretical studies on virulence-transmission trade-offs and evolution in vector-borne pathogen-host systems. Here, we consider an immuno-epidemiological model that links the within-host dynamics to between-host circulation of a vector-borne disease. On the immunological scale, the model mimics antibody-pathogen dynamics for arbovirus diseases, such as Rift Valley fever and West Nile virus. The within-host dynamics govern transmission and host mortality and recovery in an age-since-infection structured host-vector-borne pathogen epidemic model. By considering multiple pathogen strains and multiple competing host populations differing in their within-host replication rate and immune response parameters, respectively, we derive evolutionary optimization principles for both pathogen and host. Invasion analysis shows that the [Formula: see text] maximization principle holds for the vector-borne pathogen. For the host, we prove that evolution favors minimizing case fatality ratio (CFR). These results are utilized to compute host and pathogen evolutionary trajectories and to determine how model parameters affect evolution outcomes. We find that increasing the vector inoculum size increases the pathogen [Formula: see text], but can either increase or decrease the pathogen virulence (the host CFR), suggesting that vector inoculum size can contribute to virulence of vector-borne diseases in distinct ways.