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In this paper, a mathematical model for the transmission dynamics of Fasciola hepatica in cattle and snail populations is formulated and analyzed. The snail mortality rate (μs) is the most important factor that indirectly impacts the basic reproduction number (R0). A 50% change, either an increase or decrease, in the snail mortality rate will result in an approximate 50% change in the opposite direction in the value of R0. The model shows a forward bifurcation at R0 = 1, indicating that the disease dynamics undergo a critical transition at this threshold. This change signifies a transition from a disease‐free state to a persistent infection, highlighting the possibility of a continuous disease presence given specific epidemiological conditions. Simulations show that reducing miracidia, metacercariae, and snail populations, improving treatment, and lowering pathogen transfer between cattle and snails significantly decrease disease prevalence in cattle. To control the disease, transmission rates for cattle and snails must be reduced below γc = 1.4338 × 10−7 and γs = 1.1473 × 10−8, respectively. Current treatments are insufficient, and a combination of improved treatments reduced transmission rates, and increased snail mortality is recommended for better disease control. [ABSTRACT FROM AUTHOR]

In this paper, we developed a mathematical model for the dynamics of coronavirus disease (COVID‐19) transmission. The model embraces the notion of contact tracing and contaminated surfaces which are vital for disease control and contribute to disease transmission, respectively. We analyzed the model properties such as the positivity of the solution, invariant region, existence, and stability nature of equilibria. Besides, we computed the basic reproduction number R0. The local stability and the global stability of disease‐free equilibrium (DFE) points are proved by using the Routh–Hurwitz criteria and the Castillo‐Chavez and Song approach, respectively. LaSalle's invariant principle is applied to prove the stability of an endemic equilibrium (EE) point. The possibility of bifurcation is discussed using the center manifold theory. We used real data on the spread and control of COVID‐19 disease in Ethiopia. Based on the data reported, we estimated the values of the parameters using the least squares method together with the fmin function in the MATLAB optimization toolbox. The sensitivity analysis of the model is explored numerically to illustrate the impact of the parameters on disease transmission. The study addressed that contact tracing is especially important because COVID‐19 often has asymptomatic carriers, and there are many asymptomatic individuals unaware in Ethiopia. The new infections would decrease in the communities by detecting and isolating COVID‐19 cases before they could spread the virus to others. Moreover, the study endorsed that the contaminated surface has contributed to disease transmission. The sensitivity analysis shows that if the rate of disinfected contaminated objects (ϕ) rises, then the transmission of the disease is reduced. Consequently, this study will aid in the fight against COVID‐19 policymakers and NGOs. It can also be used as a policy input for different countries under this crisis. Because of the mathematical modeling of this global pandemic, there is another point of view rather than public health research outputs. Additionally, with the concept of contact tracing and contaminated surfaces incorporated into the model, the result provides insight for disease prevention. [ABSTRACT FROM AUTHOR]

Gumboro disease is a viral poultry disease that causes immune suppression on the infected birds leading to poor production, mortality, and exposure to secondary infections, hence a major threat in the poultry industry worldwide. A mathematical model of the transmission dynamics of Gumboro disease is developed in this paper having four compartments of chicken population and one compartment of Gumboro pathogen population. The basic reproduction number R og is derived, and the dynamical behaviors of both the disease-free equilibrium (DFE) and endemic equilibrium are analyzed using the ordinary differential equation theory. From the analysis, we found that the system exhibits an asymptotic stable DFE whenever R og < 1 and an asymptotic stable EE whenever R og > 1. The numerical simulation to verify the theoretical results was carried out using MATLAB ode45 solver, and the results were found to be consistent with the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper focuses on the impact of mosquito biting bias on the success of malaria intervention strategies. The initial model is developed considering the existence of symptomatic and asymptomatic humans, as well as vector bias. The model is then analyzed to demonstrate how the malaria-endemic equilibrium always exists and is globally asymptotically stable if the basic reproduction number is larger than one. On the other hand, malaria will always go extinct in the population if the basic reproduction number is less than one. For intervention analysis, the model is extended by considering mosquito repellent and hospitalization as control strategies. The control reproduction number is shown analytically. Using the Pontryagin maximum principle, we characterize our optimal control problem. Several scenarios are conducted to observe the dynamics of control variables under different circumstances. We found that the intervention of mosquito repellent and hospitalization together is the most cost-effective strategy to reduce the spread of malaria. Furthermore, we have shown that the more biased the vector attracted to infected individuals, the higher the cost needed to implement the control strategy. [ABSTRACT FROM AUTHOR]

Given that the Crimean and Congo hemorrhagic fever is one of the deadly viral diseases that occur seasonally due to the activity of the carrier "tick," studying and developing a mathematical model simulating this illness are crucial. Due to the delay in the disease's incubation time in the sick individual, the paper involved the development of a mathematical model modeling the transmission of the disease from the carrier to humans and its spread among them. The major objective is to comprehend the dynamics of illness transmission so that it may be controlled, as well as how time delay affects this. The discussion of every one of the solution's qualitative attributes is included. According to the established basic reproduction number, the stability analysis of the endemic equilibrium point and the disease-free equilibrium point is examined for the presence or absence of delay. Hopf bifurcation's triggering circumstance is identified. Using the center manifold theorem and the normal form, the direction and stability of the bifurcating Hopf bifurcation are explored. The next step is sensitivity analysis, which explains the set of control settings that have an impact on how the system behaves. Finally, to further comprehend the model's dynamical behavior and validate the discovered analytical conclusions, numerical simulation has been used. [ABSTRACT FROM AUTHOR]

Mathematical analysis of epidemics is crucial for long‐term disease prediction and helps to guide decision‐makers in terms of public health policy. In this study, we develop a within‐host mathematical model of the malaria parasite dynamics with the effect of an adaptive immune response. The model includes six compartments, namely, the uninfected red blood cells, infected red blood cells, merozoites, gametocytes, cytotoxic T cells immune response, and antibodies immune response, which are activated in the host to attack the parasite. We establish the well‐posedness and biological feasibility of the model in terms of proving the non‐negativity and boundedness of solutions. The most important threshold value in the epidemiological model known as the basic reproduction number, R0, which is used to determine the stability of the steady state, is investigated. Furthermore, the parasite‐free equilibrium is locally and globally stable if the basic reproduction number, R0<1, otherwise, if R0>1, then there exist four parasite‐persistence equilibria. The stability conditions of these parasite‐persistence equilibria are presented. Sensitivity analysis of the basic reproduction number shows that parameters representing the recruitment rate of uninfected red blood cells, infection rate of red blood cells by merozoites, and the average number of merozoites per ruptured infected red blood cells are the most influential ones in affecting the dynamics. Finally, several numerical simulations of the model are presented to supplement the theoretical and analytical findings. It has been observed that numerical simulations and theoretical results are coherent. The response of cytotoxic T cells and antibodies has a significant impact on suppressing infected cells and malaria parasites in the host's body. [ABSTRACT FROM AUTHOR]

In this study, we proposed and analyzed a nonlinear deterministic mathematical model of malaria transmission dynamics. In addition to the previous approaches, we incorporated the class of aware people and other control measures. We established the wellposedness of the model, and the asymptotic behavior of the solutions is rigorously studied depending on the basic reproduction number R0. The model system admits two equilibrium points: disease‐free and disease‐persistent equilibrium points. The analytical result of the model system revealed that the disease‐free equilibrium point is both locally as well as globally asymptotically stable whenever R0 < 1 while the disease‐persistence equilibrium point is globally asymptotically stable whenever R0 > 1. Moreover, the forward bifurcation phenomenon of the model system for R0 = 1 was analyzed by using center manifold theory. A sensitivity analysis of the basic reproduction number was performed to identify parameters that will cause to trigger the transmission of malaria disease and should be targeted by control strategies. Then, the model was extended to the optimal control problem, with the use of three time‐dependent controls, namely, preventive measures(treated bednets and indoor residual spraying), continuous awareness campaigns to susceptible individuals, and treatment for infected individuals. By using Pontryan's maximum principle, necessary conditions for the transmission of malaria disease were derived. Numerical simulations are illustrated by using MATLAB ode45 to validate the theoretical results of the model. The numerical findings of the optimal model suggested that integrated control strategies are better than a sole intervention to eliminate malaria disease. [ABSTRACT FROM AUTHOR]

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 > 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. [ABSTRACT FROM AUTHOR]

This work presents a stochastic model of malaria spread. We first calculated the basic reproduction number R 0 of the models S h I h R h S h ‐ S v I v and S h L h I h R h S h ‐ S v L v I v in order to show that the malaria-free equilibrium is asymptotically stable; then, we used a finite Markov chain model to describe the interactions between the different compartments of the model S e L e I e R e S e ‐ S a L a I a R a S a ‐ S v I v . We carried out numerical simulations of our results for two types of transmission zones: a zone with low malaria transmission and an endemic zone. Through these simulations, we first determined the invariant stationary distribution π ∗ of the model, and then, we found that the use of the indoor residual spraying (IRS) method by regular application of insecticides is more effective for the elimination of malaria than the use of long-acting impregnated mosquito nets (LLINs). [ABSTRACT FROM AUTHOR]

Coccidiosis is an infectious disease caused by the Eimeria species. The species can infect a bird's digestive system, severely slow down its growth, and is a serious economic burden for chickens. A mathematical model for the transmission dynamics of coccidiosis disease in chickens in the presence of control interventions has been formulated and analyzed to gain insights into the dynamics of the disease in the population. Three control interventions, namely vaccination, sanitation, and treatment, are implemented. The study intends to assess the effects of these control interventions in coccidiosis transmission dynamics. Using the theory of differential equations, the invariant set of the model was derived, and the model's solution was found to be mathematically and biologically significant. Analytical methods are employed to establish equilibrium solutions and investigate the stability of the model system's equilibria, while numerical simulations illustrate the analytical results. The effective reproduction number is obtained using the next-generation matrix method, and the local stability of the equilibria of the model is established. The disease-free equilibrium is proved to be locally stable when the effective reproduction number is less than unity. Also, the nature of the bifurcation and its implications for disease prevention are investigated through the application of the center manifold theory. On the other hand, sensitivity analysis is carried out to investigate the parameters that impact the transmission of coccidiosis disease using the normalized forward sensitivity index. The parameters that have a greater influence on the effective reproduction number should be targeted for control purposes to lessen the spread of disease. Furthermore, numerical simulation is performed to investigate the contribution of each control intervention. [ABSTRACT FROM AUTHOR]

Malaria is a complex disease with many factors influencing the transmission dynamics, including age. This research analyzes the transmission dynamics of malaria by developing an age-structured mathematical model using the classical integer order and Atangana–Baleanu–Caputo fractional operators. The analysis of the model focused on several important aspects. The existence and uniqueness of solutions of fractional order were explored based on some fixed-point theorems,such as Banach and Krasnoselski. The Positivity and boundedness of the solutions were also investigated. Furthermore, through mathematical analysis techniques, we analyzed different types of stability results, and the results showed that the disease-free equilibrium point of the model is proved to be both locally and globally asymptotically stable if the basic reproduction number is less than one, whereas the endemic equilibrium point of the model is both locally and globally asymptotically stable if the basic reproduction number is greater than one. The findings from the sensitivity analysis revealed that the most sensitive parameters, essential for controlling or eliminating malaria are mosquito biting rate, density-dependent natural mortality rate, clinical recovery rate, and recruitment rate for mosquitoes. Numerical simulations are also performed to examine the behavior of the model for different values of the fractional-order alpha,and the result revealed that as the value α reduces from 1, the spread of the endemic grows slower. By incorporating these findings, this research helps to clarify the dynamics of malaria and provides information on how to create efficient control measures. [ABSTRACT FROM AUTHOR]