Journal of Biological Dynamics

We investigate the dynamics of a prey-predator model with cooperative hunting among specialist predators and maturation delay in predator growth. First, we consider a model without delay and explore the effect of hunting time on the coexistence of predator and their prey. When the hunting time is long enough and the cooperation rate among predators is weak, prey and predator species tend to coexist. Furthermore, we observe the occurrences of a series of bifurcations that depend on the cooperation rate and the hunting time...

In this paper, we develop discrete models of Tuberculosis (TB). This includes SEI endogenous and exogenous models without treatment. These models are then extended to a SEIT model with treatment. We develop two types of net reproduction numbers, one is the traditional <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub></mml:math> which is based on the disease-free equilibrium, and a new net reproduction number <mml:math xmlns:mml="https://www...

The adaptive immune system has two types of plasma cells (PC), long-lived plasma cells (LLPC) and short-lived plasma cells (SLPC), that differ in their lifespan. In this paper, we propose that LLPC is crucial to the clearance of viral particles in addition to reducing the viral basic reproduction number in secondary infections. We use a sequence of within-host mathematical models to show that, CD8 T cells, SLPC and memory B cells cannot achieve full viral clearance, and the viral load will reach a low positive equilibrium level because of a continuous replenishment of target cells...

In this study, we apply optimal control theory to an immuno-epidemiological model of HIV and opioid epidemics. For the multi-scale model, we used four controls: treating the opioid use, reducing HIV risk behaviour among opioid users, entry inhibiting antiviral therapy, and antiviral therapy which blocks the viral production. Two population-level controls are combined with two within-host-level controls. We prove the existence and uniqueness of an optimal control quadruple. Comparing the two population-level controls, we find that reducing the HIV risk of opioid users has a stronger impact on the population who is both HIV-infected and opioid-dependent than treating the opioid disorder...

Throughout the last two centuries, vaccines have been helpful in mitigating numerous epidemic diseases. However, vaccine hesitancy has been identified as a substantial obstacle in healthcare management. We examined the epidemiological dynamics of an emerging infection under vaccination using an SVEIR model with differential morbidity. We mathematically analyzed the model, derived <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub></mml:math>, and provided a complete analysis of the bifurcation at <mml:math xmlns:mml="https://www...

Symptomatic and asymptomatic individuals play a significant role in the transmission dynamics of novel Coronaviruses. By considering the dynamical behaviour of symptomatic and asymptomatic individuals, this study examines the temporal dynamics and optimal control of Coronavirus disease propagation using an epidemiological model. Biologically and mathematically, the well-posed epidemic problem is examined, as well as the threshold quantity with parameter sensitivity. Model parameters are quantified and their relative impact on the disease is evaluated...

When initially introduced into a susceptible population, a disease may die out or result in a major outbreak. We present a Continuous-Time Markov Chain model for enzootic WNV transmission between two avian host species and a single vector, and use multitype branching process theory to determine the probability of disease extinction based upon the type of infected individual initially introducing the disease into the population - an exposed vector, infectious vector, or infectious host of either species. We explore how the likelihood of disease extinction depends on the ability of each host species to transmit WNV, vector biting rates on host species, and the relative abundance of host species, as well as vector abundance...

In this paper, a compartmental model on the co-infection of pneumonia and HIV/AIDS with optimal control strategies was formulated using the system of ordinary differential equations. Using qualitative methods, we have analysed the mono-infection and HIV/AIDS and pneumonia co-infection models. We have computed effective reproduction numbers by applying the next-generation matrix method, applying Castillo Chavez criteria the models disease-free equilibrium points global stabilities were shown, while we have used the Centre manifold criteria to determine that the pneumonia infection and pneumonia and HIV/AIDS co-infection exhibit the phenomenon of backward bifurcation whenever the corresponding effective reproduction number is less than unity...

We study an avascular spherical solid tumour model with cell physiological age and resource constraints in vivo. We divide the tumour cells into three components: proliferating cells, quiescent cells and dead cells in necrotic core. We assume that the division rate of proliferating cells is nonlinear due to the nutritional and spatial constraints. The proportion of newborn tumour cells entering directly into quiescent state is considered, since this proportion can respond to the therapeutic effect of drug. We establish a nonlinear age-structured tumour cell population model...

Ehrlichia chaffeensis is a tick-borne disease transmitted by ticks to dogs. Few studies have mathematical modelled such tick-borne disease in dogs, and none have developed models that incorporate different ticks' developmental stages (discrete variable) as well as the duration of infection (continuous variable). In this study, we develop and analyze a model that considers these two structural variables using integrated semigroups theory. We address the well-posedness of the model and investigate the existence of steady states...

The region of St. Louis, Missouri, has displayed a high level of heterogeneity in COVID-19 cases, hospitalization, and vaccination coverage. We investigate how human mobility, vaccination, and time-varying transmission rates influenced SARS-CoV-2 transmission in five counties in the St. Louis area. A COVID-19 model with a system of ordinary differential equations was developed to illustrate the dynamics with a fully vaccinated class. Using the weekly number of vaccinations, cases, and hospitalization data from five counties in the greater St...

In this paper, we formulate a population suppression model and a population replacement model with periodic impulsive releases of Nilaparvata   lugens infected with wStri . The conditions for the stability of wild-<mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi><mml:mo>.</mml:mo><mml:mspace/><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>g</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>s</mml:mi></mml:math>-eradication periodic solution of two systems are obtained by applying the Floquet theorem and comparison theorem...

We formulate simple differential equation models to study the impact of releases of transgenic sterile mosquitoes carrying a dominant lethal on mosquito control based on the modified sterile insects technique. The early acting bisex, late acting bisex, early acting female-killing, and late acting female-killing lethality strategies are all considered. We determine release thresholds of the transgenic sterile mosquitoes, respectively, for these models by investigating the existence of positive equilibria and their stability...

HIV continues to be a major global health issue, having claimed millions of lives in the last few decades. While several empirical studies support the fact that proper nutrition is useful in the fight against HIV, very few studies have focused on developing and using mathematical modelling approaches to assess the association between HIV, human immune response to the disease, and nutrition. We develop a within-host model for HIV that captures the dynamic interactions between HIV, the immune system and nutrition...

The work of Fred Brauer (1932-2021) broke new ground in several areas of mathematical population biology, especially mathematical epidemiology and population management. This special issue reflects his legacy: the lines of inquiry he opened, the impact of his research and his books, and his mentoring of generations of young researchers. This dedication highlights milestones in his career and connects his work to the contributions in this issue.

In this paper, we investigate a reaction-diffusion model incorporating dynamic variables for nutrient, phytoplankton, and zooplankton. Moreover, we account for the impact of time delay in the growth of phytoplankton following nutrient uptake. Our theoretical analysis reveals that the time delay can trigger the emergence of persistent oscillations in the model via a Hopf bifurcation. We also analytically track the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Our simulation results demonstrate stability switches occurring for the positive equilibrium with an increasing time lag...

In volume transmission (or neuromodulation) neurons do not make one-to-one connections to other neurons, but instead simply release neurotransmitter into the extracellular space from numerous varicosities. Many well-known neurotransmitters including serotonin (5HT), dopamine (DA), histamine (HA), Gamma-Aminobutyric Acid (GABA) and acetylcholine (ACh) participate in volume transmission. Typically, the cell bodies are in one volume and the axons project to a distant volume in the brain releasing the neurotransmitter there...

Chemotaxis is a directed cell movement in response to external chemical stimuli. In this paper, we propose a simple model for the origin of chemotaxis - namely how a directed movement in response to an external chemical signal may occur based on purely reaction-diffusion equations reflecting inner working of the cells. The model is inspired by the well-studied role of the rho-GTPase Cdc42 regulator of cell polarity, in particular in yeast cells. We analyse several versions of the model to better understand its analytic properties and prove global regularity in one and two dimensions...

No abstract text is available yet for this article.

Leishmaniasis, an infectious disease, manifests itself mostly in two forms, cutaneous leishmaniasis (CL) and, a more severe and potentially deadly form, visceral leishmaniasis (VL). The current control strategy for leishmaniasis relies on chemotherapy drugs such as sodium antimony gluconate (SAG) and meglumine antimoniate (MA). However, all these chemotherapy compounds have poor efficacy, and they are associated with toxicity and other adverse effects, as well as drug resistance. While research in vaccine development for leishmaniasis is continuously progressing, no vaccine is currently available...