Partial Rank Correlation Research Articles

Global Sensitivity Analysis of A Rabies Epidemic Model involving Dog Vaccination and Dog Population Management

Rabies is a zoonotic disease which is spread by animals mostly carnivores. Rabies regards as tropic disease. In this article, we construct a mathematical model for rabies involving dog vaccination and dog population management. The model has two equilibrium points, namely rabies-free equilibrium point and endemic equilibrium point. We determine the effective reproduction ratio using next generation matrix. Our dynamical analysis shows that rabies-free equilibrium point is conditionally stable. A global sensitivity analysis is performed to investigate which intervention is the most crucial among the two interventions considered in the model. We use Latin hypercube sampling method to generate parameter space. To investigate the parameter sensitivity, we calculate the partial rank correlation coefficient. We provide numerical experimental results related to stability and global sensitivity analysis. Our results show that the effective reproduction ratio is more sensitive to dog population management than vaccination intervention. This suggests that dog population management intervention, such as sterilization and monitoring of dog movements significantly reduces the effective reproduction ratio compared to vaccination programs. In addition, the number of infectious dogs has a strong correlation with dog culling actions.

Deficits in force production during multifinger tasks demarcate cognitive dysfunction

BackgroundThe multifinger force deficit (MFFD) is the decline in force generated by each finger as the number of fingers contributing to an action is increased. It has been shown to associate with cognitive status.AimsThe aim was to establish whether a particularly challenging form of multifinger grip dynamometry, that provides minimal tactile feedback via cutaneous receptors and requires active compensation for reaction forces, will yield an MFFD that is more sensitive to cognitive status.MethodsAssociations between measures of motor function, and cognitive status (Montreal Cognitive Assessment [MoCA]) and latent components of cognitive function (derived from 11 tests using principal component analysis), were estimated cross-sectionally using generalized partial rank correlations. The participants (n = 62) were community dwelling, aged 65–87.ResultsApproximately half the participants were unable to complete the dynamometry task successfully. Cognitive status demarcated individuals who could perform the task from those who could not. Among those who complied with the task requirements, the MFFD was negatively correlated with MoCA scores—those with the highest MoCA scores tended to exhibit the smallest deficits, and vice versa. There were corresponding associations with latent components of cognitive function.DiscussionThe results support the view that neurodegenerative processes that are a feature of normal and pathological aging exert corresponding effects on expressions of motor coordination—in multifinger tasks, and cognitive sufficiency, due to their dependence on shared neural systems.ConclusionsThe outcomes add weight to the assertion that deficits in force production during multifinger tasks are sensitive to cognitive dysfunction.

Estimating groundwater geogenic arsenic contamination and the affected population of river basins underlain mostly with crystalline rocks in Ghana

Arsenic is a human carcinogen and contributes to the incidences of cancer, diabetes, and skin diseases in the exposed populations. Therefore, its occurrence in drinking water is of public health concern worldwide, especially in the Tano, Pra, and Ankobra River Basins in Ghana. The metasediments and metavolcanic formations which underlie these basins (42,092.5 km2) host arsenic sulphide minerals that are a source of arsenic contamination of the weathered and fractured aquifers that serve as drinking water supply to most of the population (∼9.8 million), especially in the rural areas. A random forest machine learning method and partial dependence plots were applied to maps of spatially continuous environmental factors (fault density, surface bulk density, coarse fragment and soil pH; and sub-surface silt and soil pH) and hydrochemical variables, respectively, and arsenic measurements from wells (n = 229) which included 57 new datasets of which 7.86 % exceeded the 10 µg/L to develop arsenic prediction models for the basins at thresholds of 1 µg/L, 5 µg/L, and 10 µg/L. Fault density and coarse fragments were more reliable contributors to the models. A partial dependence plot and Spearman's rank correlation analysis showed a significant positive correlation (p < 0.01) between arsenic enrichment and HCO3−, pH, Fe, and Mn, except NO3− in groundwater. Arsenic hotspots occurred in urban districts in the Ashanti Region and known gold-mining areas in Nzema, Obuasi, Prestea, and Tarkwa. Spatially, arsenic contamination in groundwater covered 49.44 % of the land area of the basins. By cross-referencing population density estimates and the arsenic hazard map,15.8 % of the population is exposed to arsenic-contaminated groundwater in the basins. The hazard model will facilitate efforts to reduce rural poverty and protect public health by delivering potable water in Ghana. The hazard models apply to crystalline terrain in other sub-Saharan African countries.

Assessing the impact of information-induced self-protection on Zika transmission: A mathematical modeling approach

Abstract As per the World Health Organization’s (WHO’s) suggestions, personal protection via adopting precautionary measures is one of the most effective control aspects to avoid Zika infection in the absence of suitable medical treatment. This personal protection further can be enhanced and explored by propagating information about disease prevalence. Therefore, in this study, we wish to see the effect of information on Zika transmission by formulating a compartmental mathematical model that quantifies the effect of an individual’s behavioral response as self-protection due to information. Furthermore, the basic reproduction number was calculated using the next-generation matrix technique. The model analysis was carried out to determine the local and global stability properties of equilibrium points. In addition, the model shows the occurrence of forward bifurcation when the reproduction number crosses unity. To understand the impact of various model parameters, we conducted a sensitivity analysis using both the normalized sensitivity index and the partial rank correlation coefficient methods. Moreover, we performed numerical simulations to assess the influence of important parameters on the model’s behavior for Zika prevalence. Our study accentuates that as information-induced self-protection increases, the prevalence of Zika infection will be at a very minimum level, and this observation is in line with WHO suggestions.

Mutations make pandemics worse or better: modeling SARS-CoV-2 variants and imperfect vaccination.

COVID-19 is a respiratory disease triggered by an RNA virus inclined to mutations. Since December 2020, variants of COVID-19 (especially Delta and Omicron) continuously appeared with different characteristics that influenced death and transmissibility emerged around the world. To address the novel dynamics of the disease, we propose and analyze a dynamical model of two strains, namely native and mutant, transmission dynamics with mutation and imperfect vaccination. It is also assumed that the recuperated individuals from the native strain can be infected with mutant strain through the direct contact with individual or contaminated surfaces or aerosols. We compute the basic reproduction number, , which is the maximum of the basic reproduction numbers of native and mutant strains. We prove the nonexistence of backward bifurcation using the center manifold theory, and global stability of disease-free equilibrium when , that is, vaccine is effective enough to eliminate the native and mutant strains even if it cannot provide full protection. Hopf bifurcation appears when the endemic equilibrium loses its stability. An intermediate mutation rate leads to oscillations. When increases over a threshold, the system regains its stability and exhibits an interesting dynamics called endemic bubble. An analytical expression for vaccine-induced herd immunity is derived. The epidemiological implication of the herd immunity threshold is that the disease may effectively be eradicated if the minimum herd immunity threshold is attained in the community. Furthermore, the model is parameterized using the Indian data of the cumulative number of confirmed cases and deaths of COVID-19 from March 1 to September 27 in 2021, using MCMC method. The cumulative cases and deaths can be reduced by increasing the vaccine efficacies to both native and mutant strains. We observe that by considering the vaccine efficacy against native strain as 90%, both cumulative cases and deaths would be reduced by 0.40%. It is concluded that increasing immunity against mutant strain is more influential than the vaccine efficacy against it in controlling the total cases. Our study demonstrates that the COVID-19 pandemic may be worse due to the occurrence of oscillations for certain mutation rates (i.e., outbreaks will occur repeatedly) but better due to stability at a lower infection level with a larger mutation rate. We perform sensitivity analysis using the Latin Hypercube Sampling methodology and partial rank correlation coefficients to illustrate the impact of parameters on the basic reproduction number, the number of cumulative cases and deaths, which ultimately sheds light on disease mitigation.

Metabolic symbiosis between oxygenated and hypoxic tumour cells: An agent-based modelling study.

Deregulated metabolism is one of the hallmarks of cancer. It is well-known that tumour cells tend to metabolize glucose via glycolysis even when oxygen is available and mitochondrial respiration is functional. However, the lower energy efficiency of aerobic glycolysis with respect to mitochondrial respiration makes this behaviour, namely the Warburg effect, counter-intuitive, although it has now been recognized as source of anabolic precursors. On the other hand, there is evidence that oxygenated tumour cells could be fuelled by exogenous lactate produced from glycolysis. We employed a multi-scale approach that integrates multi-agent modelling, diffusion-reaction, stoichiometric equations, and Boolean networks to study metabolic cooperation between hypoxic and oxygenated cells exposed to varying oxygen, nutrient, and inhibitor concentrations. The results show that the cooperation reduces the depletion of environmental glucose, resulting in an overall advantage of using aerobic glycolysis. In addition, the oxygen level was found to be decreased by symbiosis, promoting a further shift towards anaerobic glycolysis. However, the oxygenated and hypoxic populations may gradually reach quasi-equilibrium. A sensitivity analysis using Latin hypercube sampling and partial rank correlation shows that the symbiotic dynamics depends on properties of the specific cell such as the minimum glucose level needed for glycolysis. Our results suggest that strategies that block glucose transporters may be more effective to reduce tumour growth than those blocking lactate intake transporters.

Mathematical modelling, analysis and numerical simulation of social media addiction and depression.

We formulate a mathematical model of social media addiction and depression (SMAD) in this study. Key aspects, such as social media addiction and depression disease-free equilibrium point (SMADDFEP), social media addiction and depression endemic equilibrium point (SMADEEP), and basic reproduction number (R0), have been analyzed qualitatively. The results indicate that if R0 < 1, the SMADDFEP is locally asymptotically stable. The global asymptotic stability of the SMADDFEP has been established using the Castillo-Chavez theorem. On the other hand, if R0 > 1, the unique endemic equilibrium point (SMADEEP) is locally asymptotically stable by Lyapunov theorem, and the model exhibits a forward bifurcation at R0 = 1 according to the Center Manifold theorem. To examine the model's sensitivity, we calculated the normalized forward sensitivity index and conducted a Partial Rank Correlation Coefficient (PRCC) analysis to describe the influence of parameters on the SMAD. The numerical results obtained using the Fourth-order Runge-Kutta (RK-4) scheme show that increasing the number of addicted individuals leads to an increase in the number of depressed individuals.

GLOBAL SENSITIVITY ANALYSIS AND OPTIMAL CONTROL OF TYPHOID FEVER TRANSMISSION DYNAMICS

This paper presents a mathematical model aimed at studying the global behaviour and optimal control strategies for Typhoid fever. The primary objective of this study is to identify the most effective control strategy that minimizes the spread of the disease. To achieve this, we calculate the effective and basic reproduction numbers and utilize them to investigate the existence and stability of the equilibria. Furthermore, we investigate the global impact of each model parameter on the variables using Latin Hypercube Sampling and Partial Rank Correlation Coefficient. The necessary conditions of the optimal control problem are analyzed using Pontryagin’s maximum principle, and the numerical values of the model parameters are estimated using the maximum likelihood estimator. The results indicate that the optimal use of vaccination for susceptible individuals, as well as the screening and treatment of asymptomatic infected individuals, have a significant impact on reducing the spread of the disease in endemic regions.

Association of multi-phase rates of force development during an isometric leg press with vertical jump performances.

This study aimed to elucidate characteristics of explosive force-production capabilities represented by multi-phase rate of force developments (IRFDs) during isometric single-leg press (ISLP) through investigating relationships with countermovement (CMJ) and rebound continuous jump (RJ) performances. Two-hundred-and-thirty male athletes performed ISLP, CMJ with an arm swing (CMJAS), and RJ with an arm swing (RJAS). IRFDs were measured during ISLP using a custom-built dynamometer, while CMJAS and RJAS were measured on force platforms. The IRFDs were obtained as rates of increase in force across 50 ms in the interval from the onset to 250 ms. Jump height (JH) was obtained from CMJAS, while RJAS provided JH, contact time (CT), and reactive strength index (RSI) values. All IRFDs were correlated with CMJAS-JH (ρ = 0.20-0.45, p ≤ 0.003), RJAS-JH (ρ = 0.22-0.46, p ≤ 0.001), RJAS-RSI (ρ = 0.29-0.48, p < 0.001) and RJAS-CT (ρ = -0.29 to -0.25, p ≤ 0.025). When an influence of peak force was considered using partial rank correlation analysis, IRFDs during onset to 150 ms were correlated with CMJAS-JH (ρxy/z = 0.19-0.36, p ≤ 0.004), IRFDs during onset to 100 ms were correlated with RJAS-JH and RJAS-RSI (ρxy/z = 0.33-0.36, p < 0.001), and IRFD during onset to 50 ms was only correlated with RJAS-CT (ρxy/z = -0.23, p < 0.001). The early phase (onset to 150 ms) IRFDs measured using ISLP enabled the assessment of multiple aspects of leg-extension strength characteristics that differ from maximal strength; these insights might be useful in the assessment of the athletes' leg-extension strength capabilities.

Decreased retinal vascular density is associated with cognitive impairment in CADASIL: an optical coherence tomography angiography study.

This study aimed to assess alterations in retinal vascular density in cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy (CADASIL) patients using optical coherence tomography angiography (OCTA) and investigate their association with MRI and cognitive features. Twenty-five patients with CADASIL and forty healthy controls were evaluated by Cirrus HD-OCT 5000 with AngioPlex OCTA to determine changes in macular retinal vasculature. Retinal vasculature parameters between two groups were compared. The MRI lesion burden and neuropsychological scales were also examined in patients. The association between OCTA parameters and MRI/cognitive features was evaluated using partial Spearman rank correlation. The vessel density and perfusion density of whole image in macular region (vessel density: t = - 2.834, p = 0.005; perfusion density: t = - 2.691, p = 0.007) were significantly decreased in patients with CADASIL. Moreover, vessel density of whole image in macular region was negatively associated with Fazekas scores (ρ = - 0.457; p = 0.025) and the number of lacunar infractions (ρ = - 0.425, p = 0.038) after adjustment for age. Decreased macular vessel density and perfusion density of whole image were also associated with MoCA scores (vessel density: ρ = 0.542, p = 0.006; perfusion density: ρ = 0.478, p = 0.018) and other domain-specific neuropsychological tests (p < 0.05) after adjustment for age. Decreased retinal vascular density was associated with increased MRI lesion burden and cognitive impairment in patients with CADASIL. Our findings suggest that the degree of retinal vascular involvement, as demonstrated by OCTA, may be consistent with the severity of MRI lesions and the degree of cognitive impairment in patients.

ENDEAVORING THE ROLE OF OBESITY IN EXTRACELLULAR MATRIX DEGRADATION LEADING TO METASTASIS

One of the significant causes of death globally is cancer ( http://www.who.org/ ). Another critical problem is obesity, which is associated with an increased cancer threat. This work provides insight into how obesity contributes to cancer progression and metastasis. We developed a diffusive obesity-cancer model consisting of cancer cells, normal cells, fat cells, macrophages, and an extracellular matrix (ECM) for this aim. We have directed the formed model’s global existence and non-negativity. Equilibrium points for the related ODE are calculated, and its existence and stability study is also done. We present a traveling wave analysis of the obesity-cancer model and have calculated the minimum wave speed. Using a combination of analytic and numerical results of traveling waves, we conjecture that the minimal wave speed depends on fat cells’ diffusive rate and haptotaxis coefficient. We followed the theory of the Partial Rank Correlation Coefficient (PRCC) to carry out a global sensitivity analysis to evaluate the most sensitive parameters reliable for cancer progression. We delivered a comprehensive numerical analysis of our deterministic and diffusive models (in 1D and 2D) and analogized the result. Numerical simulation of corresponding spatially explicit systems conveys complex spatio-temporal dynamics, resulting in the appearance of patterns. It also discloses that cancer spread increases with increased haptotaxis coefficient and growth rate of obese cells. Our simulation confirms that the degradation of the ECM increases cancer spread and density.

Modelling of tuberculosis dynamics incorporating indirect transmission of contaminated environment and infectivity of smear-negative individuals: A case study for Xinjiang, China

Xinjiang has been one of the high incidence areas of pulmonary tuberculosis (PTB) in China. Besides being infected by direct contacting with active PTB individuals (direct infection), the susceptible would be infected because of the exposure to the environment contaminated by Mycobacterium tuberculosis (indirect infection). Active PTB individuals include not only the smear-positive PTB (PTB+) but also the smear-negative PTB (PTB–) who are infectious due to their ability to release tiny Mycobacterium tuberculosis particles even in the absence of visible Mycobacterium tuberculosis in sputum. By taking account of direct/indirect infection and the difference between PTB+ and PTB– individuals in transmission capability, a periodic dynamical PTB transmission model is proposed. The model is fitted to the newly monthly PTB+ and PTB– cases in Xinjiang from 2008 to 2017 by Markov Chain Monte Carlo algorithm. Moreover, global sensitivity analysis is constructed to address the uncertainty of some key parameters by using Latin hypercube sampling and partial rank correlation coefficient methods. Basic reproduction number R0 for PTB transmission in Xinjiang is estimated to be 2.447 (95% CrI:(1.203, 3.844)), indicating that PTB has been prevalent in Xinjiang over the study period. Our results suggest that reducing the direct/indirect transmission rates, early screening, isolating and treating the latent, PTB+ and PTB– individuals, and enhancing the clearance of Mycobacterium tuberculosis in the environment could more effectively control PTB transmission in Xinjiang. The model fits the reported PTB data well and achieves acceptable prediction accuracy. We believe that our model can provide heuristic support for controlling PTB transmission in Xinjiang.

Transmission Dynamics of Monkeypox Virus With Age‐Structured Human Population: A Mathematical Modeling Approach

This study presents a deterministic mathematical model of monkeypox disease transmission dynamics with an age‐structured human population divided into two subgroups of children (Group 1) and adults (Group 2). Two equilibrium points, monkeypox‐free, E0, and a unique monkeypox‐endemic equilibrium point, E1, are established. The age‐structured monkeypox basic reproduction number, ℝ0, is computed using the next‐generation matrix approach and established to be ℝ0 = 1.2448. The Lyapunov functions are constructed; together with LaSalle’s invariance principle, the monkeypox‐free equilibrium point, E0, is established to be globally asymptotically stable whenever ℝ0 ≤ 1, as confirmed by the Lyapunov stability method, and the monkeypox‐endemic equilibrium point, E1, is globally asymptotically stable whenever ℝ0 &gt; 1. Sensitivity analysis of the threshold quantity ℝ0 is performed using the Latin hypercube sampling method and Pearson’s partial rank correlation coefficient, and the results showed that the parameters β11, β22, μ, ν1, Λ1, ν2 were the most sensitive to the spread of monkeypox infection in an age‐structured population. It is, therefore, suggested that the rate of monkeypox infection can be reduced by ensuring that the rate of interaction between susceptible children and infected children and between susceptible adults and infected adults is minimized. Moreover, the spread of monkeypox infection can be curbed by emphasizing controls such as early diagnosis and treatment and hospitalization of critically ill infectives.

Hopf bifurcation and hybrid control of a delayed diffusive semi-ratio-dependent predator-prey model

&lt;p&gt;A delayed diffusive predator-prey system with nonmonotonic functional response subject to Neumann boundary conditions is introduced in this paper. First, we analyze the associated characteristic equation to research the conditions for local stability of the positive equilibrium point and the occurrence of Turing instability induced by diffusion in the absence of delay. Second, we provide conditions for the existence of Hopf bifurcation driven by time delay. By utilizing the normal theory and center manifold theorem, we derive explicit formulas for Hopf bifurcation properties such as direction and stability from the positive equilibrium. Third, a hybrid controller is added to the system. By judiciously adjusting the control parameters, we effectively enhance the stability domain of the system, resulting in a modification of the position of the Hopf bifurcation periodic solutions. Numerical simulations demonstrate the presence of rich dynamical phenomena within the system. Moreover, sensitivity analysis was conducted using Latin hypercube sampling (LHS)/partial rank correlation coefficient (PRCC) to explore the impact of parameter variations on the output of prey and predator populations.&lt;/p&gt;

Mathematical model of tuberculosis with seasonality, detection, and treatment

In this study, we use a modified SEIR compartmental model to investigate the transmission dynamics of tuberculosis as well as its detection and treatment. The construction of this model is based on the hypothesis that the total population can be divided into seven compartments: susceptible, vaccinated, latently infected, diagnosed infected, undiagnosed infected, treated individuals, delayed treated individuals, and recovered individuals with a nonautonomous system. The effective reproduction number shows that the amplitude of the effective reproduction number decreases with the increasing vaccination rate and increases with the increase in the degree of seasonality of TB. The stability analyses of the model show that the value of the basic reproduction number R0 acts as a threshold between disease-free and endemic equilibrium. The model is found to be locally and globally asymptotically stable at the disease-free equilibrium when R0<1. On the contrary, the model is found to be locally and globally asymptotically at the endemic equilibrium when R0>1. The sensitivity of the parameters of the corresponding autonomous system is examined using the partial rank correlation coefficients (PRCC) analysis, which demonstrates that identification has a positive index and treatment has a negative index. The model is simulated using the RK-45 numerical method, and the parameter values for the model are taken from the available literature. Finally, the model outcome was compared with the real field data and found to be consistent.

Dynamics and optimal control of tuberculosis model with the combined effects of vaccination, treatment and contaminated environments.

Tuberculosis has affected human beings for thousands of years, and until today, tuberculosis still ranks third among 29 infectious diseases in China. However, most of the existing mathematical models consider a single factor, which is not conducive to the study of tuberculosis transmission dynamics. Therefore, this study considers the combined effects of vaccination, treatment, and contaminated environments on tuberculosis, and builds a new model with seven compartments of $ SVEITRW $ based on China's tuberculosis data. The study shows that when the basic reproduction number $ R_{0} $ is less than 1, the disease will eventually disappear, but when $ R_{0} $ is greater than 1, the disease may persist. In the numerical analysis part, we use Markov-chain Monte-Carlo method to obtain the optimal parameters of the model. Through the next generation matrix theory, we calculate that the $ R_{0} $ value of tuberculosis in China is $ 2.1102 $, that is, if not controlled, tuberculosis in China will not disappear over time. At the same time, through partial rank correlation coefficients, we find the most sensitive parameter to the basic reproduction number $ R_{0} $. On this basis, we combine the actual prevalence of tuberculosis in China, apply Pontryagin's maximum principle, and perform cost-effectiveness analysis to obtain the conditions required for optimal control. The analysis shows that four control strategies could effectively reduce the prevalence of TB, and simultaneously controlling $ u_{2}, u_{3}, u_{4} $ is the most cost-effective control strategy.

Non-optimal and optimal fractional control analysis of measles using real data

This study employs fractional, non-optimal, and optimal control techniques to analyze measles transmission dynamics using real-world data. Thus, we develop a fractional-order compartmental model capturing measles transmission dynamics. We then formulate an optimal control problem to minimize the disease burden while considering constraints such as vaccination resources and intervention costs. The proposed model’s positivity, boundedness, measles reproduction number, and stability are obtained. The sensitivity analysis using the partial rank correlation coefficient is shown for the fractional orders of 0.99 and 0.90. It is noticed that the rate of recruitment into the susceptible population (π), the rate at which individuals in the latent class become asymptomatic (α1), and the transmission rate (β) contribute positively to the spread of the disease, while the rate at which individuals in the asymptomatic class become symptomatic (α2), the vaccination rate for the first measles dose (γ1), and the rate at which individuals in the latent class recover from measles (δ1) contribute significantly to the reduction of measles in the community. Utilizing numerical simulations and sensitivity analyses, we identify optimal control strategies that balance the trade-offs between intervention efficacy, resource allocation, and societal costs. Our findings provide insights into the effectiveness of fractional optimal control strategies in mitigating measles outbreaks and contribute to developing more robust and adaptive disease control policies in real-world scenarios.

The role of Allee effect in cannibalistic species: An action plan to sustain the declining cod population

Atlantic cod collapsed in the late 20th century after being harvested heavily for 50 years. This paper aims to design conservation guidelines for the cod population, which is diminishing due to predation by grey seals and cannibalism. For this purpose, we first designed a continuous time ecological model (with and without the Allee effect) using a system of differential equations consisting of juvenile Atlantic cod, adult Atlantic cod, and grey seals. The developed model has set forth global existence, non-negativity, and long-term behavior. Subsequently, to handle the extinction problem cost-effectively, Pontryagin’s principle is employed to construct the optimal control, which is then numerically solved using an iterative forward–backward method. We numerically explored the impact of the Allee effect on cod survival within the original model and its two extended versions (i) stochastic and (ii) reaction–diffusion, to thoroughly understand the possible consequences wherein a population has cannibalistic tendencies. The numerical comparison between the non-Allee and Allee models (Ordinary, Stochastic, Reaction–Diffusion) reveals that the Allee effect may significantly promote recovery and benefit the cannibalistic population. We adopted a partial rank correlation coefficient (PRCC) to conduct a global sensitivity analysis to estimate the most sensitive parameters responsible for cod prevalence.

Mathematical Analysis of Malaria Epidemic: Asymptotic Stability With Cost‐Effectiveness Study

Malaria is an old, curable vector‐borne disease that is devastating in the tropics and subtropical regions of the world. The disease has unmatched complications in the human host, especially in children. Mathematical models of infectious diseases have been the steering wheel, driving scientists towards elucidation of the dynamic behaviour of epidemics and providing tailored strategic management of diseases. With the ongoing vaccination programs for vector‐borne diseases, the research proposes a nonlinear differential equation model for the malaria disease that provides public health with a shift from the classical understanding of nonpharmaceutical preventive malaria control to pharmaceutical measures of vaccines. The asymptotic dynamic behaviour of the model is studied at the model’s equilibria. The bifurcation type invoked at the disease‐free state is analysed, and the result revealed that the convention that is the condition for eradicating the disease is not always sufficient when the system undergoes backward bifurcation. Furthermore, sensitivity analysis was investigated to quantify the amount of influence each parameter has on . With the Latin hypercube sampling and partial rank correlation coefficient method, the uncertainty in is computed with a 95% confidence interval, with the mean, and 5th and 95th percentiles, respectively, simulated as 0.143788, 0.01545, and 0.41491. An intervention model was derived from the nonintervention model to experiment with and evaluate the respective effects of the various pairings of interventions on the dynamics of the disease. Lastly, an in‐depth cost analysis was studied to identify the most cost‐effective intervention regarding rewarding the desired outcome. From the analysis, we recommend that besides the nonpharmaceutical measure of bed nets and insecticide spray, public health should target the pharmaceutical intervention of vaccine as it can close the gap in malaria prevention.

Modeling and analysis of Cystic Echinococcosis epidemic model with health education

&lt;abstract&gt;&lt;p&gt;The prevention and control of the spread of Cystic Echinococcosis is an important public health issue. Health education has been supported by many governments because it can increase public awareness of echinococcosis, promote the development of personal hygiene habits, and subsequently reduce the transmission of echinococcosis. In this paper, a dynamic model of echinococcosis is used to integrate all aspects of health education. Theoretical analysis and numerical model fitting were used to quantitatively analysed by the impact of health education on the spread of echinococcosis. Theoretical findings indicate that the basic reproduction number is crucial in determining the prevalence of echinococcosis within a given geographical area. The parameters of the model were estimated and fitted by using data from the Ningxia Hui Autonomous Region in China, and the sensitivity of the basic reproduction number was analysed by using the partial rank correlation coefficient method. These findings illustrate that all aspects of health education demonstrate a negative correlation with the basic reproduction number, suggesting the effectiveness of health education in reducing the basic reproduction number and mitigating the transmission of echinococcosis, which is consistent with reality. Particularly, the basic reproduction number showed a strong negative correlation with the burial rate of infected livestock ($ b $) and the incidence of infected livestock viscera that is not fed to dogs ($ q $). This paper further analyzes the implementation plan for canine deworming rates and sheep immunity rates, as well as the transmission of infected hosts over time under different parameters $ b $ and $ q $. According to the findings, emphasizing the management of infected livestock in health education has the potential to significantly reduce the risk of echinococcosis transmission. This study will provide scientific support for the creation of higher quality health education initiatives.&lt;/p&gt;&lt;/abstract&gt;