Free terminal time optimal control of a fractional-order model for the HIV/AIDS epidemic

In this paper, we present a fractional model for the HIV/AIDS epidemic and incorporate into the model control parameters of pre-exposure prophylaxis (PrEP), behavioral change and antiretroviral therapy (ART) aimed at controlling the spread of diseases. We prove the local and global asymptotic stability of disease-free and endemic equilibria of the model. We present a general fractional optimal control problem (FOCP) with free terminal time and develop the Adapted Forward-Backward Sweep method for numerical solving of the FOCP. Necessary conditions for a state/control/terminal time triplet to be optimal are obtained. The results show that the use of all controls increases the life expectancy of HIV-treated patients with ART and remarkably increases the number of people undergoing PrEP and changing their sexual habits. Also, when the derivative order [Formula: see text] ([Formula: see text]) limits to 1, the value of optimal terminal time increases while the value of objective functional decreases.

Correlation and trust mechanisms-based rumor propagation model in complex social networks

In real life, the process of rumor propagation is influenced by many factors. The complexity and uncertainty of human psychology make the diffusion model more challenging to depict. In order to establish a comprehensive propagation model, in this paper, we take some psychological factors into consideration to mirror rumor propagation. Firstly, we use the Ridenour model to combine the trust mechanism with the correlation mechanism and propose a modified rumor propagation model. Secondly, mean-field equations which describe the dynamics of the modified SIR model on homogenous and heterogeneous networks are derived. Thirdly, a steady-state analysis is conducted for the spreading threshold and the final rumor size. Fourthly, we investigate rumor immunization strategies and obtain immunization thresholds. Next, simulations on different networks are carried out to verify the theoretical results and the effectiveness of the immunization strategies. The results indicate that the utilization of trust and correlation mechanisms leads to a larger final rumor size and a smaller terminal time. Moreover, different immunization strategies have disparate effectiveness in rumor propagation.

Robust Optimal Investment-Reinsurance Strategies for a Jump-Diffusion Risk Model with Mean-reverting Stock Return

Objectives: This paper proposes a strategy of robust optimal investment reinsurance for insurance companies. It was assumed that the surplus procedure of the insurance company satisfies the jump-diffusion procedure. Insurance companies could invest their surplus funds in the financial market consisted of both risk assets and one risk-free asset. The price procedure of risk assets satisfies the stochastic procedure with a mean reversion rate. Considering the uncertainty of the model, the ambiguity-averse insurance firm aims to enhance the exponential utility of insurance surplus at terminal time. This paper has investigated the problem of robust optimal investment reinsurance and obtained the differential equation supported by the value function.

Pengaruh Pengendalian Integrated Port Time (IPT) terhadap Kelancaran Kegiatan Bongkar Muat Di PT. Pertamina (Persero) Regional IV Semarang

Penelitian ini bertujuan untuk mengkaji pengaruh pengendalian sistem Integrated Port Time (IPT) terhadap kelancaran kegiatan bongkar muat di PT. Pertamina (Persero) Regional IV Semarang. Penulis melakukan pengamatan di PT. Pertamina (Persero) Regional IV Semarang, selain itu juga melakukanWawancara dengan orang-orang yang terkait dengan permasalahan yang dibahas tepatnya pada fungsi Marine dimana terdapat beberapa hal yang menjadi masalah dalam menjalankan sistem Integrated Port Time tersebut yaitu tingginya waktu tunggu di Pelabuhan yang berimplikasi terhadap biaya angkut, Lamanya waktu kapal di terminal dipengaruhi banyak faktor yang melibatkan fungsi Refinery Unit, S&D, Domas dan Aviasi serta Shipping. Selain itu, kendala infrastruktur darat dan kapal yang masih belum memadai mengakibatkan operasional menjadi terhambat. Penulis juga mengumpulkan literatur dari buku-buku, aturan-aturan dan penelitian yang terkait dengan Intregated Port Time dan Bongkar Muat. Hasil pembahasan menunjukkan bahwa ada Pengaruh Intregated Port Time terhadap kelancaran bongkar muat di PT. Pertamina (Persero) Regional IV Semarang. Hal ini dapat dibuktikan dengan Tingginya waktu tunggu di Pelabuhan yang merupakan salah satu penghambat Integrated Port Time (IPT), hal ini dikarenakan adanya Waiting Time, Terminal Time, Lab Time Score, Marine Time dan Finance Ops Time. Lamanya waktu kapal pada saat di terminal mengakibatkan operasi penyaluran BBM menjadi terlambat dan infrastruktur darat dan Kapal yang masih belum memadai.

Multi-time state mean-variance model in continuous time

The objective of the continuous time mean-variance model is to minimize the variance (risk) of an investment portfolio with a given mean at the terminal time. However, the investor can stop the investment plan at any time before the terminal time. To solve this problem, we consider to minimize the variances of the investment portfolio in the multi-time state. The advantage of this multi-time state mean-variance model is the minimization of the risk of the investment portfolio within the investment period. To obtain the optimal strategy of the model, we introduce a sequence of Riccati equations, which are connected by jump boundary conditions. In addition, we establish the relationships between the means and variances in the multi-time state mean-variance model. Furthermore, we use an example to verify that the variances of the multi-time state can affect the average of Maximum-Drawdown of the investment portfolio.

Stochastic model of network formation with asymmetric players

We propose a model of a network formation using the theory of stochastic games with random terminal time. Initially, the leader proposes a joint project in the form of a network to the players. Then, the players have the opportunities to form new links with each other to update the network proposed by the leader. Any player's payoff at any stage is determined by the network structure. It is also assumed that the formation of links proposed by the players is random. The duration of the game is also random. As a result of the players' actions and the implementation of the random steps of the Nature, a network is formed. We consider a cooperative approach to network formation, and we use the CIS-value as a cooperative solution. In this paper, a recurrent formula for its derivation in any cooperative subgame is obtained. The paper also investigates the dynamic consistency of CIS-value. The theoretical results are demonstrated by a numerical example.