Modeling the within-host dynamics of cholera: bacterial-viral interaction

Modelling techniques in cholera epidemiology: A systematic and critical review

Diverse modelling techniques in cholera epidemiology have been developed and used to (1) study its transmission dynamics, (2) predict and manage cholera outbreaks, and (3) assess the impact of various control and mitigation measures. In this study, we carry out a critical and systematic review of various approaches used for modelling the dynamics of cholera. Also, we discuss the strengths and weaknesses of each modelling approach. A systematic search of articles was conducted in Google Scholar, PubMed, Science Direct, and Taylor & Francis. Eligible studies were those concerned with the dynamics of cholera excluding studies focused on models for cholera transmission in animals, socio-economic factors, and genetic & molecular related studies. A total of 476 peer-reviewed articles met the inclusion criteria, with about 40% (32%) of the studies carried out in Asia (Africa). About 52%, 21%, and 9%, of the studies, were based on compartmental (e.g., SIRB), statistical (time series and regression), and spatial (spatiotemporal clustering) models, respectively, while the rest of the analysed studies used other modelling approaches such as network, machine learning and artificial intelligence, Bayesian, and agent-based approaches. Cholera modelling studies that incorporate vector/housefly transmission of the pathogen are scarce and a small portion of researchers (3.99%) considers the estimation of key epidemiological parameters. Vaccination only platform was utilized as a control measure in more than half (58%) of the studies. Research productivity in cholera epidemiological modelling studies have increased in recent years, but authors used diverse range of models. Future models should consider incorporating vector/housefly transmission of the pathogen and on the estimation of key epidemiological parameters for the transmission of cholera dynamics.

Within-Host Mathematical Models of Antibiotic Resistance

Mathematical models have been used to study the spread of infectious diseases from person to person. More recently studies are developing within-host modeling which provides an understanding of how pathogens-bacteria, fungi, parasites, or viruses-develop, spread, and evolve inside a single individual and their interaction with the host's immune system.Such models have the potential to provide a more detailed and complete description of the pathogenesis of diseases within-host and identify other influencing factors that may not be detected otherwise. Mathematical models can be used to aid understanding of the global antibiotic resistance (ABR) crisis and identify new ways of combating this threat.ABR occurs when bacteria respond to random or selective pressures and adapt to new environments through the acquisition of new genetic traits. This is usually through the acquisition of a piece of DNA from other bacteria, a process called horizontal gene transfer (HGT), the modification of a piece of DNA within a bacterium, or through. Bacteria have evolved mechanisms that enable them to respond to environmental threats by mutation, and horizontal gene transfer (HGT): conjugation; transduction; and transformation. A frequent mechanism of HGT responsible for spreading antibiotic resistance on the global scale is conjugation, as it allows the direct transfer of mobile genetic elements (MGEs). Although there are several MGEs, the most important MGEs which promote the development and rapid spread of antimicrobial resistance genes in bacterial populations are plasmids and transposons. Each of the resistance-spread-mechanisms mentioned above can be modeled allowing us to understand the process better and to define strategies to reduce resistance.

Rich dynamics of a bidirectionally linked immuno-epidemiological model for cholera

Cholera is an environmentally driven disease where the human hosts both ingest the pathogen from polluted environment and shed the pathogen to the environment, generating a two-way feedback cycle. In this paper, we propose a bidirectionally linked immuno-epidemiological model to study the interaction of within- and between-host cholera dynamics. We conduct a rigorous analysis for this multiscale model, with a focus on the stability and bifurcation properties of each feasible equilibrium. We find that the parameter that represents the bidirectional connection is a key factor in shaping the rich dynamics of the system, including the occurrence of the backward bifurcation and Hopf bifurcation. Numerical results illustrate a practical application of our model and add new insight into the prevention and intervention of cholera epidemics.

An immuno-epidemiological model linking between-host and within-host dynamics of cholera

Cholera, a severe gastrointestinal infection caused by the bacterium Vibrio cholerae, remains a major threat to public health, with a yearly estimated global burden of 2.9 million cases. Although most existing models for the disease focus on its population dynamics, the disease evolves from within-host processes to the population, making it imperative to link the multiple scales of the disease to gain better perspectives on its spread and control. In this study, we propose an immuno-epidemiological model that links the between-host and within-host dynamics of cholera. The immunological (within-host) model depicts the interaction of the cholera pathogen with the adaptive immune response. We distinguish pathogen dynamics from immune response dynamics by assigning different time scales. Through a time-scale analysis, we characterise a single infected person by their immune response. Contrary to other within-host models, this modelling approach allows for recovery through pathogen clearance after a finite time. Then, we scale up the dynamics of the infected person to construct an epidemic model, where the infected population is structured by individual immunological dynamics. We derive the basic reproduction number ($ \mathcal{R}_0 $) and analyse the stability of the equilibrium points. At the disease-free equilibrium, the disease will either be eradicated if $ \mathcal{R}_0 < 1 $ or otherwise persists. A unique endemic equilibrium exists when $ \mathcal{R}_0 > 1 $ and is locally asymptotically stable without a loss of immunity.

Mathematical Models for Cholera Dynamics-A Review

Cholera remains a significant public health burden in many countries and regions of the world, highlighting the need for a deeper understanding of the mechanisms associated with its transmission, spread, and control. Mathematical modeling offers a valuable research tool to investigate cholera dynamics and explore effective intervention strategies. In this article, we provide a review of the current state in the modeling studies of cholera. Starting from an introduction of basic cholera transmission models and their applications, we survey model extensions in several directions that include spatial and temporal heterogeneities, effects of disease control, impacts of human behavior, and multi-scale infection dynamics. We discuss some challenges and opportunities for future modeling efforts on cholera dynamics, and emphasize the importance of collaborations between different modeling groups and different disciplines in advancing this research area.

Coupling the modeling of phage-bacteria interaction and cholera epidemiological model with and without optimal control

In this work, we assess the impact of the phage-bacteria infection and optimal control on the indirectly transmitted cholera disease. The phage-bacteria interactions are described by predator-prey system using the Smith functional response, which takes into account the number of bacteria binding sites. The study is done in two steps, namely the model without control and the model with control. For the first scenario, we explicitly compute the basic reproduction number R₀ which serves as stability threshold and bifurcation parameter. The proposed model exhibits a bi-stability phenomenon via the existence of backward bifurcation, which implies that the classical requirement of bringing the reproduction number under unity, while necessary, is no longer sufficient for cholera elimination from the population. We intuitively introduce a new threshold number N₀ needed for the global stability of the disease free equilibrium point which is achieved when R₀⩽1 and N₀⩽1. It is further shown that the phage absorption is a possible cause of bi-stability, since in its absence, the condition R₀⩽1 is sufficient for cholera to die out. The existence of endemic equilibrium points depends on the range of both R₀ and N₀. Regarding the model extended to an optimal control problem, which involves the use of virulent vibriophages to reduce or eliminate the bacteria population, we use optimal control theory techniques. We establish the conditions under which the spread of cholera can be stopped, and examine the impact of control measures on the transmission dynamic of cholera. The Pontryagin's maximum principle is used to characterize the optimal control. Numerical simulations suggest that, the release of lytic vibriophages can significantly reduce the spread of the disease. We discuss opportunities for phage therapy as treatment of some bacterial-borne diseases without side effects.

Bifurcation analysis of a phage-bacteria interaction model with prophage induction

A predator-prey model is used to investigate the interactions between phages and bacteria by considering the lytic and lysogenic life cycles of phages and the prophage induction. We provide answers to the following conflictual research questions: (1) what are conditions under which the presence of phages can purify a bacterial infected environment? (2) Can the presence of phages triggers virulent bacterial outbreaks? We derive the basic offspring number $\mathcal N_0$ that serves as a threshold and the bifurcation parameter to study the dynamics and bifurcation of the system. The model exhibits three equilibria: an unstable environment-free equilibrium, a globally asymptotically stable (GAS) phage-free equilibrium (PFE) whenever $\mathcal N_0<1$, and a locally asymptotically stable environment-persistent equilibrium (EPE) when $\mathcal N_0>1$. The Lyapunov-LaSalle techniques are used to prove the GAS of the PFE and estimate the EPE basin of attraction. Through the center manifold approximation, topological types of the PFE are precised. Existence of transcritical and Hopf bifurcations are established. Precisely, when $\mathcal N_0>1$, the EPE loses its stability and periodic solutions arise. Furthermore, increasing $\mathcal N_0$ can purify an environment where bacteriophages are introduced. Purposely, we prove that for large values of $\mathcal N_0$, the overall bacterial population asymptotically approaches zero, while the phage population sustains. Ecologically, our results show that for small values of $\mathcal N_0$, the existence of periodic solutions could explain the occurrence of repetitive bacteria-borne disease outbreaks, while large value of $\mathcal N_0$ clears bacteria from the environment. Numerical simulations support our theoretical results.

Modeling Phage-Bacteria Dynamics

Phage-bacteria interaction is a classic example of competitive coevolution in nature. Mathematical modeling of such interactions furnishes new insight into the dynamics of phage and bacteria. Besides its intrinsic value, a somewhat underutilized aspect of such insight is that it can provide beneficial inputs toward better experimental design. In this chapter, we discuss several modeling techniques that can be used to study the dynamics between phages and their host bacteria. Monte Carlo simulations and differential equations (both ordinary and delay differential equations) can be used to successfully model phage-bacteria dynamics in well-mixed populations. The presence of spatial restrictions in the interaction media significantly affects the dynamics of phage-bacteria interactions. For such cases, techniques like cellular automata and reaction-diffusion equations can be used to capture these effects adequately. We discuss details of the modeling techniques with specific examples.

A multi-scale cholera model linking between-host and within-host dynamics

We propose a multi-scale modeling framework to investigate the transmission dynamics of cholera. At the population level, we employ a SIR model for the between-host transmission of the disease. At the individual host level, we describe the evolution of the pathogen within the human body. The between-host and within-host dynamics are connected through an environmental equation that characterizes the growth of the pathogen and its interaction with the hosts outside the human body. We put a special emphasis on the within-host dynamics by making a distinction for each individual host. We conduct both mathematical analysis and numerical simulation for our model in order to explore various scenarios associated with cholera transmission and to better understand the complex, multi-scale disease dynamics.