Journal of Biological Dynamics最新文献

A population model of HIV that includes susceptible individuals not taking the pre-exposure prophylaxis (PrEP), susceptible individuals taking daily PrEP, and infected individuals is developed for casual partnerships, as well as monogamous and non-monogamous long-term partnerships. Reflecting the reality of prescription availability and usage in the U.S., the PrEP taking susceptible population is a mix of individuals designated by the CDC as high and low risk for acquiring HIV. The rate of infection for non-monogamous long-term partnerships with differential susceptibility is challenging to calculate and requires Markov chain theory to represent the movement between susceptible populations before infection. The parameters associated with PrEP initiation, suspension and adherence impact both the reproduction number of the model and the elasticity indices of the reproduction model. A multi-parameter analysis reveals that increasing adherence has the largest effect on decreasing the number of new infections.

The dynamics of tuberculosis transmission model with different genders are to be established and studied. The basic regeneration numbers $R_0=R_F+R_M$ are to be defined, where $R_F$ and $R_M$ to be the basic reproduction number of tuberculosis transmission in female and male populations, respectively. The existence and global stability of the disease-free equilibrium was discussed when $R_0<1$. The global dynamic behaviours of the corresponding limit system under some conditions are to be provided, including the existence, uniqueness, and global stability of the disease-free equilibrium and endemic equilibrium. The numerical simulation shows that the endemic equilibrium may be unique and stable when $R_0>1$, and the system will undergo Hopf bifurcation based on some parameter values. Finally, we applied this model to analyse the transmission of tuberculosis in China, estimated the incidence of tuberculosis in China in 2035, and gave the conclusion that controlling the incidence of tuberculosis in male populations could better reduce the incidence of tuberculosis in China.

In this paper, we develop a non-autonomous delay differential equation model for mosquito population suppression. After establishing the positiveness and boundedness of the solutions, we study the dynamical behaviours of the model with or without Wolbachia-infected male mosquitoes. More specifically, for the model without infected male mosquitoes, we analyse the asymptotic stability of the equilibria and demonstrate that the model undergo Hopf bifurcations under certain conditions. For the model incorporating infected male mosquitoes, we derive sufficient conditions for the global asymptotic stability of the origin. Numerical examples are provided to illustrate and support our theoretical findings.

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 $R_0$ which is based on the disease-free equilibrium, and a new net reproduction number $R_0\left(E^{\ast }\right)$ based on the endemic equilibrium. It is shown that the disease-free equilibrium is globally asymptotically stable if $R_0\le 1$ and unstable if $R_0>1$. Moreover, the endemic equilibrium is locally asymptotically stable if $R_0\left(E^{\ast }\right)<1<R_0$.

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. Theoretical predictions are compared to the outcome of stochastic simulations. We find the community composition of hosts and vectors, as well as the means of disease introduction, can greatly affect the probability of disease extinction.

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 $R_0$, and provided a complete analysis of the bifurcation at $R_0=1$. Sensitivity analysis and numerical simulations were used to quantify the tradeoffs between vaccine efficacy and vaccine hesitancy on reducing the disease burden. Our results indicated that if the percentage of the population hesitant about taking the vaccine is 10%, then a vaccine with 94% efficacy is required to reduce the peak of infections by 40%. If 60% of the population is reluctant about being vaccinated, then even a perfect vaccine will not be able to reduce the peak of infections by 40%.

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. The within-host-level antiviral treatment has an effect not only on the co-affected population but also on the HIV-only infected population. Our findings suggest that the most effective strategy for managing the HIV and opioid epidemics is combining all controls at both within-host and between-host scales.

In a recent study, a mathematically identical ODE model is derived from a multiscale PDE model of hepatitis C virus infection, which helps to overcome the limitations of the PDE model in the analysis. Here, an extended proposed model is formulated for this transformed ODE model by including the hepatocyte proliferation of both uninfected and infected cells. Unlike the transformed model, the proposed model can predict the triphasic viral decline and the virus level after therapy cessation without oscillations. Numerical simulations are performed to investigate the effect of hepatocyte proliferation and therapy with direct-acting antivirals agents (DAAs). The basic reproduction number is obtained, the equilibrium points are specified, and their stability is analysed. A bifurcation analysis is performed to specify the bifurcation points and to study the effect of varying system parameters. Various viral load profiles generated by the model are confirmed to fit with reported data in the literature.