Mathematical Biosciences最新文献

We introduce a class of discrete single species models with distributed delay in the reproductive process and a cohort dependent survival function that accounts for survival pressure during that delay period. These delay recurrences track the mature population for species in which individuals reach maturity after at least $\tau$ and at most $\tau +{\tau }_M$ breeding cycles. Under realistic model assumptions, we prove the existence of a critical delay threshold, ${\tilde{\tau }}_c$. For given delay kernel length ${\tau }_M$, if each individual takes at least ${\tilde{\tau }}_c$ time units to reach maturity, then the population is predicted to go extinct. We show that the positive equilibrium is decreasing in both $\tau$ and ${\tau }_M$. In the case of a constant reproductive rate, we provide an equation to determine ${\tilde{\tau }}_c$ for fixed ${\tau }_M$, and similarly, provide a lower bound on the kernel length, ${\tilde{\tau }}_M$ for fixed $\tau$ such that the population goes extinct if ${\tau }_M\ge {\tilde{\tau }}_M$. We compare these critical thresholds for different maturation distributions and show that if all else is the same, to avoid extinction it is best if all individuals in the population have the shortest delay possible. We apply the model derivation to a Beverton–Holt model and discuss its global dynamics. For this model with kernels that share the same mean delay, we show that populations with the largest variance in the time required to reach maturity have higher population levels and lower chances of extinction.

We model interactions between cancer cells and viruses during oncolytic viral therapy. One of our primary goals is to identify parameter regions that yield treatment failure or success. We show that the tumor size under therapy at a particular time is less than the size without therapy. Our analysis demonstrates two thresholds for the horizontal transmission rate: a “failure threshold” below which treatment fails, and a “success threshold” above which infection prevalence reaches 100% and the tumor shrinks to its smallest size. Moreover, we explain how changes in the virulence of the virus alter the success threshold and the minimum tumor size. Our study suggests that the optimal virulence of an oncolytic virus depends on the timescale of virus dynamics. We identify a threshold for the virulence of the virus and show how this threshold depends on the timescale of virus dynamics. Our results suggest that when the timescale of virus dynamics is fast, administering a more virulent virus leads to a greater reduction in the tumor size. Conversely, when the viral timescale is slow, higher virulence can induce oscillations with high amplitude in the tumor size. Furthermore, we introduce the concept of a “Hopf bifurcation Island” in the parameter space, an idea that has applications far beyond the results of this paper and is applicable to many mathematical models. We elucidate what a Hopf bifurcation Island is, and we prove that small Islands can imply very slowly growing oscillatory solutions.

Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these kinetic models often relies on Boltzmann’s “molecular chaos” hypothesis, which assumes that correlations between individuals are short-lived. While this assumption is often the simplest way to derive tractable models, it is often not valid in practice due to the high levels of cooperation and self-organization present in biological systems. In this work, we illustrated this point by considering a general Boltzmann-type kinetic model for the alignment of self-propelled rods where rod reorientation occurs upon binary collisions. We examine the accuracy of the kinetic model by comparing numerical solutions of the continuous equations to an agent-based model that implements the underlying rules governing microscopic alignment. Even for the simplest case considered, our comparison demonstrates that the kinetic model fails to replicate the discrete dynamics due to the formation of rod clusters that violate statistical independence. Additionally, we show that introducing noise to limit cluster formation helps improve the agreement between the analytical model and agent simulations but does not restore the agreement completely. These results highlight the need to both develop and disseminate improved moment-closure methods for modeling biological and active matter systems.

Understanding the interplay between social activities and disease dynamics is crucial for effective public health interventions. Recent studies using coupled behavior-disease models assumed homogeneous populations. However, heterogeneity in population, such as different social groups, cannot be ignored. In this study, we divided the population into social media users and non-users, and investigated the impact of homophily (the tendency for individuals to associate with others similar to themselves) and online events on disease dynamics. Our results reveal that homophily hinders the adoption of vaccinating strategies, hastening the approach to a tipping point after which the population converges to an endemic equilibrium with no vaccine uptake. Furthermore, we find that online events can significantly influence disease dynamics, with early discussions on social media platforms serving as an early warning signal of potential disease outbreaks. Our model provides insights into the mechanisms underlying these phenomena and underscores the importance of considering homophily in disease modeling and public health strategies.

Schistosomiasis, a freshwater-borne neglected tropical disease, disproportionately affects impoverished communities mainly in the tropical regions. Transmission involves humans and intermediate host (IH) snails. This manuscript introduces a mathematical model to probe schistosomiasis dynamics and the role of non-host snail competitors and predators as biological control agents for IH snails. The numerical analyses include investigations into steady-state conditions and reproduction numbers associated with uncontrolled scenarios, as well as scenarios involving non-host snail competitors and/or predators. Sensitivity analysis reveals that increasing snail mortality rates is a key to reducing the IH snail population and control of the transmission. Results show that specific snail competitors and/or predators with strong competition/predation abilities reduce IH snails and the subsequent infectious cercaria populations, reduce the transmission, and possibly eradicate the disease, while those with weaker abilities allow disease persistence. Hence our findings advocate for the effectiveness of snail competitors with suitable competitive pressures and/or predators with appropriate predatory abilities as nature-based solutions for combating schistosomiasis, all while preserving IH snail biodiversity. However, if these strategies are implemented at insignificant levels, IH snails can dominate, and disease persistence may pose challenges. Thus, experimental screening of potential (native) snail competitors and/or predators is crucial to assess the likely behavior of biological agents and determine the optimal biological control measures for IH snails.

In epidemiology, realistic disease dynamics often require Susceptible-Exposed-Infected-Recovered (SEIR)-like models because they account for incubation periods before individuals become infectious. However, for the sake of analytical tractability, simpler Susceptible-Infected-Recovered (SIR) models are commonly used, despite their lack of biological realism. Bridging these models is crucial for accurately estimating parameters and fitting models to observed data, particularly in population-level studies of infectious diseases.

This paper investigates stochastic versions of the SEIR and SIR frameworks and demonstrates that the SEIR model can be effectively approximated by a SIR model with time-dependent infection and recovery rates. The validity of this approximation is supported by the derivation of a large-population Functional Law of Large Numbers (FLLN) limit and a finite-population concentration inequality.

To apply this approximation in practice, the paper introduces a parameter inference methodology based on the Dynamic Survival Analysis (DSA) survival analysis framework. This method enables the fitting of the SIR model to data simulated from the more complex SEIR dynamics, as illustrated through simulated experiments.

The continual social and economic impact of infectious diseases on nations has maintained sustained attention on their control and treatment, of which self-medication has been one of the means employed by some individuals. Self-medication complicates the attempt of their control and treatment as it conflicts with some of the measures implemented by health authorities. Added to these complications is the stigmatization of individuals with some diseases in some jurisdictions. This study investigates the co-infection of COVID-19 and malaria and its related deaths and further highlights how self-medication and stigmatization add to the complexities of the fight against these two diseases using Nigeria as a study case. Using a mathematical model on COVID-19 and malaria co-infection, we address the question: to what degree does the impact of the interaction between COVID-19 and malaria amplify infections and deaths induced by both diseases via self-medication and stigmatization? We demonstrate that COVID-19 related self-medication due to misdiagnoses contributes substantially to the prevalence of disease. The control reproduction numbers for these diseases and quantification of model parameters uncertainties and sensitivities are presented.

In this paper, we introduce a stochastic two-strain epidemic model driven by Lévy noise describing the interaction between four compartments; susceptible, infected individuals by the first strain, infected ones by the second strain and the recovered individuals. The forces of infection, for both strains, are represented by saturated incidence rates. Our study begins with the investigation of unique global solution of the suggested mathematical model. Then, it moves to the determination of sufficient conditions of extinction and persistence in mean of the two-strain disease. In order to illustrate the theoretical findings, we give some numerical simulations.

The ecological relationship among plants, rhizobacteria and plant consumers has attracted the attention of researchers due to its implications in field crops. It is known that, the rhizosphere is occupied not only by rhizobacteria which grant benefits to the plants but also by bacteria which are detrimental for them. In this work, we construct and analyze a plants–rhizobacteria–plant consumers system. In the modeling process, it is assumed that there is a conditioned interaction between plants and bacteria in the rhizosfera such that there is a mutualistic relationship at low densities of rhizobacteria and the relationship is parasitic or competitive at higher densities of them. Benefits granted by rhizobacteria include mechanisms that increase the plant growth and defense mechanisms against plant consumers. From the analysis of the model and its simplified version, we show that scenarios of coexistence of all populations can occur for a wide range of values of the parameters which describe biotic or abiotic factors; however, these scenarios are in risk since scenarios of exclusion of species can occur simultaneously due to the presence of bistability phenomena. The results obtained can be useful for the decision makers to design interventions strategies on field crops when plant growth-promoting rhizobacteria are used.

We extend the unstructured homogeneously mixing epidemic model introduced by Lamprinakou et al. (2023) to a finite population stratified by age bands. We model the actual unobserved infections using a latent marked Hawkes process and the reported aggregated infections as random quantities driven by the underlying Hawkes process. We apply a Kernel Density Particle Filter (KDPF) to infer the marked counting process, the instantaneous reproduction number for each age group and forecast the epidemic’s trajectory in the near future. Taking into account the individual inhomogeneity in age does not increase significantly the computational cost of the proposed inference algorithm compared to the cost of the proposed algorithm for the homogeneously unstructured epidemic model. We demonstrate that considering the individual heterogeneity in age, we can derive the instantaneous reproduction numbers per age group that provide a real-time measurement of interventions and behavioural changes of the associated groups. We illustrate the performance of the proposed inference algorithm on synthetic data sets and COVID-19-reported cases in various local authorities in the UK, and benchmark our model to the unstructured homogeneously mixing epidemic model. Our paper is a “demonstration” of a methodology that might be applied to factors other than age for stratification.