The Role of Coinfection in Multi-Disease Dynamics

Applied Mathematics and Computation, 2005

This paper considers a basic model for a spread of two diseases in a population. The equilibria of the model are found, and their stability is investigated. In particular, we prove the stability result for a disease-free and a one-disease steady-states. Bifurcation diagrams are used to analyse the stability of possible branches of equilibria, and also they indicate the existence of a co-infected equilibrium with both diseases present. Finally, numerical simulations of the model are performed to study the behaviour of the solutions in different regions of the parameter space.

Journal of Interdisciplinary Mathematics, 2020

This paper presents an analytical study for eco-epidemiological competition model between two proposed populations, the first is healthy while the second is infected by epidemic disease. We assumed that the type of the epidemic disease for the second population is susceptible-infected-recovered (SIR) which can be transmitted through contact only within the same population and is not transmitable to the first population. The existence of all the equilibrium points (Eps) are determined and discussed along with the uniqueness of the trajectory. In addition, the trajectory boundaries are investigated and finally, the stability (locally and gobally) conditions for all the feasible EPs are studied.

EPL (Europhysics Letters), 2013

Modeling epidemic dynamics plays an important role in studying how diseases spread, predicting their future course, and designing strategies to control them. In this letter, we introduce a model of SIR (susceptible-infected-removed) type which explicitly incorporates the effect of cooperative coinfection. More precisely, each individual can get infected by two different diseases, and an individual already infected with one disease has an increased probability to get infected by the other. Depending on the amount of this increase, we prove different threshold scenarios. Apart from the standard continuous phase transition for single-disease outbreaks, we observe continuous transitions where both diseases must coexist, but also discontinuous transitions are observed, where a finite fraction of the population is already affected by both diseases at the threshold. All our results are obtained in a mean field model using rate equations, but we argue that they should hold also in more general frameworks.

The article considers the reaction-diffusion equations modeling the infection of several interacting kinds of species by many types of bacteria. When the infected species compete significantly among themselves, it is shown by bifurcation method that the infected species will coexist with bacterial populations. The time stability of the postitive steady-states are also considered by semigroup method. If the infected species do not interact, it is shown that positive coexistence states with bacterial populations are still possible.

Electronic Journal of Differential …, 2000

The article considers the reaction-diffusion equations modeling the infection of several interacting kinds of species by many types of bacteria. When the infected species compete significantly among themselves, it is shown by bifurcation method that the infected species will coexist with bacterial populations. The time stability of the postitive steady-states are also considered by semigroup method. If the infected species do not interact, it is shown that positive coexistence states with bacterial populations are still possible.

Journal of Mathematical Biology, 2003

We consider a model for a disease with a progressing and a quiescent exposed class and variable susceptibility to super-infection. The model exhibits backward bifurcations under certain conditions, which allow for both stable and unstable endemic states when the basic reproduction number is smaller than one.

Bulletin of Mathematical Biology

In this paper, a two-strain model with coinfection that links immunological and epidemiological dynamics across scales is formulated. On the within host scale, the two strains eliminate each other with the strain having the larger immunological reproduction number persisting. However, on the population scale coinfection is a common occurrence. Individuals infected with strain one can become coinfected with strain two and similarly for individuals originally infected with strain two. The immunological reproduction numbers R j , the epidemiological reproduction numbers R j and invasion reproduction numbers R i j are computed. Besides the disease-free equilibrium, there are strain one and strain two dominance equilibria. The disease-free equilibrium is locally asymptotically stable when the epidemiological reproduction numbers R j are smaller than one. In addition, each strain dominance equilibrium is locally asymptotically stable if the corresponding epidemiological reproduction number is larger than one and the invasion reproduction number of the other strain is smaller than one. The coexistence equilibrium exists when all the reproduction numbers are greater than one. Simulations suggest that when both invasion reproduction numbers are smaller than one, bistability occurs with one of the strains persisting or the other, depending on initial conditions.

JSIAM Letters

This paper presents an epidemic model with capacities of treatment and vaccination to discuss their effect on the disease spread. It is numerically shown that a backward bifurcation occurs in the basic reproduction number R0, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when R0 < 1, if the capacities are relatively small. This epidemiological implication is that, when there is not enough capacity for treatment or vaccination, the requirement R0 < 1 is not sufficient for effective disease control and disease outbreak may happen to a high endemic level even though R0 < 1.

Letters in Biomathematics

We consider a system of non-linear differential equations describing the spread of an epidemic in two interacting populations. The model assumes that the epidemic spreads within the first population, which in turn acts as a reservoir of infection for the second population. We explore the conditions under which the epidemic is endemic in both populations and discuss the global asymptotic stability of the endemic equilibrium using a Lyapunov function and results established for asymptotically autonomous systems. We discuss monkeypox as an example of an emerging disease that can be modelled in this way and present some numerical results representing the model and its extensions.

2021

This paper presents a disease-severity-structured epidemic model with treatment necessary only to severe infective individuals to discuss the effect of the treatment capacity on the disease transmission. It is shown that a backward bifurcation occurs in the basic reproduction number R0, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when R0 &lt; 1, if the capacity is relatively small. This epidemiological implication is that, when there is not enough capacity for treatment, the requirement R0 &lt; 1 is not sufficient for effective disease control and disease outbreak can happen to a high endemic level even though R0 &lt; 1.