Roles of different update strategies in the vaccination behavior on two-layered networks

Epidemic spreading has been widely investigated over the past decades. And voluntary vaccination has been often utilized to explore dynamical process in epidemics where vaccines are available. In this letter, we establish a framework considering conformity motivated update as well as myopic best response motivated update on a family network which is demonstrated by a two-layered network. Extensive numerical simulations are conducted to study the dynamics of epidemic spreading under the aforementioned update rules, from which we discover the oscillation phenomenon under the pure myopic best response condition and the amplitude diversification phenomenon under the mixing of conformity and myopic best response motivated conditions. Moreover, we find that smaller overlapping fraction of links on two-layered network shall promote the epidemic propagation. The current findings can shed some lights on the evolution of epidemic spreading process in the real-world scenarios.     

Dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps

In this paper, the dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps is considered. Besides a standard geometric Brownian motion, another two driving processes are taken into account: a stationary Poisson point process and a continuous time finite-state Markov chain. Firstly, we establish sufficient conditions for persistence in the mean of the disease. Then we obtain sufficient conditions for extinction of the disease. In addition, we also establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.     

A novel time delayed HIV/AIDS model with vaccination & antiretroviral therapy and its stability analysis

In this paper, we propose a novel time delayed HIV/AIDS mathematical model and further analyze the effect of vaccination and ART (antiretroviral therapy) on this time delayed model, in which the time delay is due to the strong immune response to AIDS for the HIV-infected-aware because of the good physical conditions. We introduce the different stages of the period of AIDS infection having different abilities of transmitting disease, which reflects the developing progress of AIDS infection more realistically. By using suitable Lyapunov functionals and the LaSalle invariant principle, we obtain the basic reproduction number _R0${\mathfrak{R}}_0$ and derive that if _R0<1${\mathfrak{R}}_0<1$ and some parameters satisfy a given condition, the disease-free equilibrium is globally asymptotically stable, while the disease will be died out. Numerical simulations are carried out to verify the obtained stability criteria and demonstrate the effect of the vaccination rate and _R0${\mathfrak{R}}_0$ and the ART on the infective individuals.     

Optimal control and numerical methods for hybrid stochastic SIS models

This work focuses on optimal controls of a class of stochastic SIS epidemic models under regime switching. By assuming that a decision maker can influence the infectivity period, our aim is to minimize the expected discounted cost due to illness, medical treatment, and the adverse effect on the society. In addition, a model with the incorporation of vaccination is proposed. Numerical schemes are developed by approximating the continuous-time dynamics using Markov chain approximation methods. It is demonstrated that the approximation schemes converge to the optimal strategy as the mesh size goes to zero. Numerical examples are provided to illustrate our results.     

Enhancement of immune response and protection in BALB/c mice immunized with liposomal recombinant major surface glycoprotein of Leishmania (rgp63): The role of bilayer composition

Development of new generation vaccines requires adjuvants to elicit the type and intensity of immune response needed for protection. Liposomes have been shown to be an effective adjuvant formulation. In this study, the role of liposome bilayer composition with different phase transition temperature (T_c) to induce a T helper 1 (Th1) type of immune response and protection against leishmaniasis in BALB/c mice was assessed. Liposome formulations with different bilayer compositions consisting of egg phosphatidylcholine (EPC, T_c < 0 °C), dipalmitoylphosphatidylcholine (DPPC, T_c 41 °C), or distearoylphosphatidylcholine (DSPC, T_c 54 °C) were prepared. All liposomes were contained rgp63 as a recombinant antigen and used to immunize mice subcutaneously 3 times in 3-week intervals. Evaluation of lesion development and splenic parasite burden after challenge with L. major, evaluation of Th1 cytokine (IFN-γ) and Th2 cytokine (IL-4), and titration of IgG isotypes were carried out to assess the type of generated immune response and extent of protection. The results indicated the generated immune response in mice was influenced by the bilayer composition of liposomes, so that mice immunized with liposomes consisting of EPC induced a Th2 type of immune response while liposome consisting of DPPC or DSPC induced Th1 type of immune response. It seems that liposomes prepared with higher Tm phospholipids are suitable formulation to induce Th1 type of immune response and protection, and so might be used for further investigations to develop an effective vaccine against leishmaniasis.     

Three kinds of TVS in a SIR epidemic model with saturated infectious force and vertical transmission

Three different vaccination and treatment strategies in the SIR epidemic model with saturated infectious force and vertical transmission are analyzed. The dynamics of epidemic models are globally investigated by using Floquet theory and comparison theorem of impulsive differential equation. Thresholds are identified and global stability results are proved. For every treatment and vaccination strategy, the disease-free periodic solution of impulsive system has been obtained and is found to be globally asymptotically stable when the basic reproduction number is less than one, equivalently the cure rate is larger than the threshold value, whereas the disease is persistent when the basic reproduction number is larger than one. These results indicate that a large cure rate will lead to the eradication of a disease.     

Effective vaccination strategies for realistic social networks

We consider the effectiveness of targeted vaccination at preventing the spread of infectious disease in a realistic social network. We compare vaccination strategies based on no information (random vaccination) to complete information (PageRank) about the network. The most effective strategy we find is to vaccinate those people with the most unvaccinated contacts. However, this strategy requires considerable information and computational effort which may not be practical. The next best strategies vaccinate people with many contacts who in turn have few contacts.