In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

Diphtheria, a potentially life-threatening infectious disease, is primarily caused by the bacterium Corynebacterium diphtheriae. This pathogen induces a range of severe symptoms, including respiratory distress, cardiac arrhythmias, and, in extreme cases, fatal outcomes. This paper aim to unravel the transmission dynamics of diphtheria infection within the Caputo fractional derivatives framework, establishing the solutions’ existence and uniqueness. Through forward normalized sensitivity analysis, we scrutinize the key parameters influencing the basic reproduction number, a pivotal metric in understanding and controlling the spread of the disease. The results indicate that reducing the values of the interaction rate, transmission rate, and birth rate plays a key role in curtailing diphtheria transmission. Furthermore, employing an effective numerical tool, we present graphical representations that delineate the influence of various crucial model parameters on infection dynamics.

Diphtheria is a severely infectious and deadly bacterial disease with Corynebacterium diphtheriae as the causative agent. Since the COVID-19 pandemic, contagious diseases such as diphtheria have re-emerged due to disruptions in routine childhood immunization programs worldwide. Nigeria is witnessing a significant increase in diphtheria outbreaks likely due to an inadequate health care system and insufficient public enlightenment campaign. This paper presents a mathematical epidemic diphtheria model in Nigeria, which includes a public enlightenment campaign to assess its positive impact on the prevalence of the disease. The mathematical analysis of the model reveals two equilibrium points: the diphtheria infection-free equilibrium and the endemic equilibrium. These equilibrium points are shown to be stable globally asymptotically if ${\mathcal{R}}_c<1$ and ${\mathcal{R}}_c>1$, respectively. The model was fit using the confirmed diphtheria cases data of Kano State from January to December 2023. Sensitivity analysis indicates that the transmission rate and recovery rate of asymptomatic peopleare crucial parameters to be considered in developing effective strategies for diphtheria control and prevention. This analysis also reveals that the implementation of a high-level public enlightenment campaign and its high efficacy effectively reduce the prevalence of diphtheria. Finally, numerical simulations show that combining the public enlightenment campaign and isolating infected individuals is the best strategy to contain the spread of diphtheria.

In this research work, we study a new class of $\psi$-Hilfer hybrid fractional integro-differential boundary value problems with three-point boundary conditions. An existence result is established by using a generalization of Krasnosel’skiĭ’s fixed point theorem. An example illustrating the main result is also constructed.

The sugar industry is of great importance to the Thai economy. In general, the government sets sugarcane prices at the beginning of each harvesting season based on type (fresh or fired), sweetness (sugar content) and gross weight. The main aim of the present research is to use optimal control to find optimal sugarcane harvesting policies for fresh and fired sugarcane for the four sugarcane producing regions of Thailand, namely North, Central, East and North-east, for harvesting seasons 2012/13, 2013/14, 2014/15, 2017/18 and 2018/19. The optimality problem is to determine the harvesting policy which gives maximum profit to the farmers subject to constraints on the maximum amount that can be cut in each day, where a harvesting policy is defined as the amount of each type of sugarcane harvested and delivered to the sugar factories during each day of a harvesting season. The results from the optimal control methods are also compared with results from three optimization methods, namely bi-objective, linear programming and quasi-Newton. The results suggest that discrete optimal control is the most effective of the five methods considered. The data used in this paper were obtained from the Ministry of Industry and the Ministry of Agriculture and Co-operatives of the Royal Thai government.

This study develops a deterministic two-sex compartmental model to investigate the population-level effects of continuous sterile-male releases on Anopheles mosquitoes. The model distinguishes aquatic stages, unmated females, fertile-mated females, sterile-mated females, wild males, and released sterile males, while incorporating density-dependent aquatic recruitment, sex-specific adult emergence, natural mortality, and mating competition between wild and sterile males. We establish the nonnegativity and boundedness of solutions and characterise the wild-mosquito-free and nontrivial wild-mosquito equilibria. The wild-mosquito-free equilibrium is locally asymptotically stable because viable reproduction requires the joint presence of unmated females and wild males, generating a mate-finding Allee effect near extinction. Accordingly, population persistence is characterised by an explicit release-dependent threshold rather than a conventional infectious-disease reproduction number. When the intrinsic demographic condition $\mathcal{Q}>1$ holds, two nontrivial wild-mosquito equilibria may coexist below the critical release rate. Numerical eigenvalue calculations at sampled baseline release levels identify the lower branch as unstable and the upper branch as locally asymptotically stable. A center-manifold/Lyapunov–Schmidt argument establishes a nondegenerate saddle–node bifurcation of the full six-dimensional system at the critical continuous release rate. Numerical simulations are consistent with bistability under subcritical releases and show suppression of the selected established wild population under the sustained supercritical scenarios examined here; these observations are not asserted as a global convergence theorem. For the illustrative baseline parameter set, the critical release rate is approximately 1850 sterile males per day. One-at-a-time and Latin-hypercube/partial rank correlation analyses identify recruitment, maturation, adult survival, sterile-male mortality, and mating competitiveness as major determinants of the release requirement and post-intervention mosquito abundance. Although the numerical threshold is not an operational release recommendation, the framework provides an analytically transparent basis for evaluating continuous sterile-insect interventions and identifying the parameters requiring reliable field estimation.