On the Role of Short-Term Animal Movements on the Persistence of Brucellosis

Optimal Control and Cost-Effective Analysis of a Scabies Model with Direct and Indirect Transmissions

Scabies is caused by sarcoptes scabiei var. hominis, which is also referred to as itch mice. The disease is transmitted through direct contact with an infected person, or from contact with infested bedding or clothing. In this paper, a mathematical model for the spread of scabies was proposed and analyzed. Sensitivity analysis of the model parameters was carried out. Optimal control theory was applied to our proposed model, with the controls representing treatment and vaccination. Our aim was to minimize cumulative infectious cases and susceptible individuals through treatment and vaccination, respectively. Pontryagin’s maximum principle was utilized to characterize the optimal levels of the two controls. The resulting optimality system was then solved numerically. The optimal control result was further highlighted by applying the results realized from the cost objective functional, the IAR, and the ICER.

A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity

This paper proposes a model for brucellosis transmission. The model takes into account the age of infection and waning immunity, that is, the progressive loss of immunity after recovery. Three routes of transmissions are considered: vertical transmission, and both direct and indirect routes of horizontal transmission. According to the well-posedness results, we provide explicit formulas for the equilibria. Next, we derive the basic reproduction number R0 and prove some stability results depending on the basic reproductive number. Finally, we perform numerical simulations using model parameters estimated from biological data to confirm our theoretical results. The results of these simulations suggest that for certain values of parameters, there will be periodic outbreaks of epidemics, and the disease will not be eradicated from the population. Our results also highlight the fact that the birth rate of cattle significantly influences the dynamics of the disease. The proposed model can be of a good use in studying the effects of vaccination on the cattle population.

Mathematical Modeling and Optimal Control of the Hand Foot Mouth Disease Affected by Regional Residency in Thailand

Hand, foot and mouth disease (HFMD) is a virulent disease most commonly found in East and Southeast Asia. Symptoms include ulcers or sores, inside or around the mouth. In this research, we formulate the dynamic model of HFMD by using the SEIQR model. We separated the infection episodes where there is a higher outbreak and a lower outbreak of the disease associated with regional residency, with the higher level of outbreak occurring in the urban region, and a lower outbreak level occurring in the rural region. We developed two different optimal control programs for the types of outbreaks. Optimal Control Policy 1 (OPC1) is limited to the use of treatment only, whereas Optimal Control Policy 2 (OPC2) includes vaccination along with the treatment. The Pontryagin’s maximum principle is used to establish the necessary and optimal conditions for the two policies. Numerical solutions are presented along with numerical sensitivity analyses of the required control efforts needed as the control parameters are changed. Results show that the time tmax required for the optimal control effort to stay at the maximum amount umax exhibits an intrinsic logarithmic relationship with respect to the control parameters.

Transmission dynamics of brucellosis: Mathematical modelling and applications in China

Brucellosis, the most common zoonotic disease worldwide, represents a great threat to animal husbandry with the potential to cause enormous economic losses. Meanwhile, brucellosis is one of the major public-health problems in China, and the number of human brucellosis cases has increased dramatically in recent years. In order to show the main features of brucellosis transmission in China, we give a systematic review on the transmission dynamics of brucellosis including a series of mathematical models and their applications in China. For different situations, dynamical models of brucellosis transmission in single population and multiple populations are devised based on ordinary differential equations. Furthermore, we revealed the spatial-temporal characteristics and effective control measures of brucellosis transmission. The results may provide new perspectives for the prevention and control of other types of zoonoses.

Backward Bifurcation and Optimal Control Analysis of a Trypanosoma brucei rhodesiense Model

In this paper, a mathematical model for the transmission dynamics of Trypanosoma brucei rhodesiense that incorporates three species—namely, human, animal and vector—is formulated and analyzed. Two controls representing awareness campaigns and insecticide use are investigated in order to minimize the number of infected hosts in the population and the cost of implementation. Qualitative analysis of the model showed that it exhibited backward bifurcation generated by awareness campaigns. From the optimal control analysis we observed that optimal awareness and insecticide use could lead to effective control of the disease even when they were implemented at low intensities. In addition, it was noted that insecticide control had a greater impact on minimizing the spread of the disease compared to awareness campaigns.