Analysis of yellow fever prevention strategy from the perspective of mathematical model and cost-effectiveness analysis

Computational and Mathematical Methods in Medicine

2022

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Malaria has produced health issues in many parts of the world. One of the reason is due to the recurrence phenomenon, which can happen years after the main infection has appeared in the human body. Furthermore, the fumigation intervention, which has become a major worry in several regions of the world, has yielded unsatisfactory results, as seen by the high number of cases reported each year in several African countries. We present a novel mathematical model that integrates tafenoquine treatments to prevent relapse in the human population and saturation fumigation to control mosquito populations in this study. The endemic threshold, also known as the basic reproduction number, is calculated analytically, as is the existence and local stability of the equilibrium points. Through careful investigation, we discovered that the malaria-free equilibrium is locally asymptotically stable if the basic reproduction number is less than one and unstable if it is greater than one. According to the sensitivity analysis, the utilization of tafenoquine treatment is inversely proportional to the basic reproduction number. Although our model never exhibits a backward bifurcation at the basic reproduction number equal to one, we have demonstrated that it is possible; when the basic reproduction number is greater than one, two stable malaria-endemic equilibrium can exist. As a result, when the basic reproduction number is more than one, the final state will be determined by the initial condition of the population. As a result, enormous temporal fumigation can shift the stability of our malaria model from a big endemic size to a smaller endemic size, which is more advantageous in terms of the malaria prevention strategy. Despite the fact that this is not a case study, the numerical results presented in this article are intended to support any theoretical analysis of current malaria eradication tactics in the field.

Section: Malaria-free Equilibrium and The Basic Reproduction Numbermentioning

confidence: 99%

Dynamical Analysis on a Malaria Model with Relapse Preventive Treatment and Saturated Fumigation

Computational and Mathematical Methods in Medicine

2022

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“…In many epidemiological models, the basic reproduction number determines the existence or disappearance of the disease. In several epidemiological models [26][27][28][29][30], the disease has a chance to die out from the population if the basic reproduction number is less than one and always exists if the basic reproduction number is larger than one. Using the next-generation method [31], the basic reproduction number of System (1) will be calculated as follows.…”

Section: The Aat-free Equilibrium and The Basic Reproduction Numbermentioning

confidence: 99%

“…With this result, we sole our adjoint system (26) backward in time with the transversality condition given. We update our control variables using the formula in (27). The iterative process continues until a convergence criterion is satisfied.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Backward Bifurcation Emerging from a Mathematical Model of African Animal Trypanosomiasis Disease in White Rhino Populations

Windyhani

2022

J. Math. Fund. Sci.

This paper introduces a mathematical model for African animal trypanosomiasis (AAT) in white rhino and tsetse fly populations. The model accommodates two types of interventions, namely infection detection and ground spraying. The dynamical system properties were thoroughly investigated to show the existence of equilibrium points, backward bifurcation, and how they are related to the basic reproduction number. We found that there is a chance that AAT may die out from the population if the basic reproduction number is smaller than one. However, the possible existence of backward bifurcation implies a condition where we may have a stable endemic equilibrium, even when the basic reproduction number is smaller than one. Hence, the basic reproduction number is no longer sufficient to guarantee the disappearance of AAT from the population. Our sensitivity analysis on the basic reproduction number showed that the interventions of infection detection and ground spraying have good potential to eradicate AAT from the population. To analyze the most effective intervention as time-dependent variable, we reconstructed our model as an optimal control problem. Numerical simulations on various scenarios were conducted for the optimal control problem. Cost-effectiveness analysis using the Average Cost-Effectiveness Ratio (ACER) and the Incremental Cost-Effectiveness Ratio (ICER) methods was performed. From the cost-effectiveness analysis, we found that ground spraying is the most cost-effective intervention to combat the spread of AAT in white rhino populations.

“…Mathematical models have been used widely by researchers to understand how vector-borne diseases spread among the population [19][20][21][22][23]. For the dengue transmission model, many authors have used mathematical modeling to guide public health strategies to control the spread of dengue.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of the impact of community ignorance on the population dynamics of dengue

Front. Appl. Math. Stat.

Puspadani

Rusin

2023

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This study proposes a dengue spread model that considers the nonlinear transmission rate to address the level of human ignorance of dengue in their environment. The SIR − UV model has been proposed, where SIR denotes the classification of the human population and UV denotes the classification of the mosquito population. Assuming that the total human population is constant, and the mosquito population is already in its steady-state condition, using the Quasi-Steady State Approximation (QSSA) method, we reduce our SIR − UV model into a more simple IR-model. Our analytical result shows that a stable disease-free equilibrium exists when the basic reproduction number is <1. Furthermore, our model also shows the possibility of a backward bifurcation. The more ignorant the society is about dengue, the higher the possibility that backward bifurcation phenomena may appear. As a result, the condition of the basic reproduction number being <1 is insufficient to guarantee the extinction of dengue in a population. Furthermore, we found that increasing the recovery rate, reducing the waning immunity rate, and mosquito life expectancy can reduce the possibility of backward bifurcation phenomena. We use dengue incidence data from Jakarta to calibrate the parameters in our model. Through the fast Fourier transform analysis, it was found that dengue incidence in Jakarta has a periodicity of 52.4, 73.4, and 146.8 weeks. This result indicates that dengue will periodically appear at least every year in Jakarta. Parameter estimation for our model parameters was carried out by assuming the infection rate of humans as a sinusoidal function by determining the three most dominant frequencies. Numerical and sensitivity analyses were conducted to observe the impact of community ignorance on dengue endemicity. From the sensitivity analysis, we found that, although a larger community ignorance can trigger a backward bifurcation, this threshold can be minimized by increasing the recovery rate, prolonging the temporal immunity, or reducing the mosquito population. Therefore, to control dengue transmission more effectively, media campaigns undertaken by the government to reduce community ignorance should be accompanied by other interventions, such as a good treatment in the hospital or vector control programs. With this combination of interventions, it will be easier to achieve a condition of dengue-free population when the basic reproduction number is less than one.