Vol. 7 No. 2 (2024)

In this paper, we explore a classical predator-prey model where the birth rate of the prey is significantly lower than the mortality rate of the predators, while also considering a limited prey population. We incorporate an environmental carrying capacity factor for the prey to account for this. Given the different timescales of the predator and prey populations, some system solutions may exhibit a fast-slow structure. We analyze this fastslow behavior using geometric singular perturbation theory (GSPT), which allows us to separate the system into fast and slow subsystems. Our research…

COVID-19 is an infectious disease primarily transmitted to individuals through direct contact with respiratory droplets. The infection, caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), continues to spread globally infecting around 776 million confirmed cases, including over 7 million deaths. Meanwhile, dengue is a vector-borne disease caused by the Flaviviridae virus and is transmitted through bites from female mosquitoes, primarily Aedes aegypti and Aedes albopictus. It is estimated that 390 million dengue virus infections occur per year caused by four distinct…

Rumors can be defined as unverified information or statements shared by people that may be positive or negative and circulate without confirmation. Since humans naturally seek factual information for social and self-enhancement purposes, rumors become an inevitable aspect of human life, including in politics, such as elections. The complexity of the electoral process, with various factors such as individual candidates, social circumstances, and particularly the media, leads to the dynamic spread of rumors in society. Thus, it is both interesting and important to understand the dynamics of…

The most reasonable way to promote individual abstinence and increase voter turnout is through campaign interventions and schemes. Our paper introduces a deterministic model that captures the dynamics of citizens exercising their right to vote and the detrimental effect of abstainers on potential voters. The existence, basic reproductive number (R0) and local stability of abstinence behavior equilibrium points are determined by certain necessary conditions. The global stability of the abstaining-free point and abstaining point is achieved through the use of suitable Lyapunov functions. In…

The gravity model which is based on Newton’s gravitational law, has been widely used as a spatial interaction model in the past few decades. Spatial interactions are important in epidemic modeling as different populations in the world are interconnected by them. Human dispersal behaviors are spatial interactions and they are crucial aspects of infectious disease spread. However, many existing compartmental models model epidemics in a single area. Hence, a gravity model approach to model epidemics incorporated with a multipatch compartmental model is studied here. Both human dispersal…

We present a delayed epidemic model in a periodic environment, taking into account behavioral changes. The model combines two types of behavioral responses: one responding to the progression of the epidemic and the other based on independent education of the epidemic. We establish the global stability of the diseasefree equilibrium and validate the model using real influenza data in Nova Scotia, Canada. Using numerical simulations, we compare the effects of behavioral changes early on with those that occur as the epidemic progresses. Our results highlight the important role of early and…

The implicit impact of vaccination on susceptible cells (epithelial layer) is studied on the basis of stability analysis of age-structured epidemic model of susceptible cells, infected cells and cells of lesion tissue (dysplasia and cancer), human papillomavirus (HPV). The efficacy of the vaccine indirectly influences the coefficients of the system, thereby determining the types of dynamical regime of the HPV and cellular population. The model possesses unique disease-free (DFE) and unique endemic equilibria (EE) (Theorem 1). The asymptotically stable DFE is associated with the resilience of…

We consider a mathematical model of cervical cancer based on the Natural History of Cervical Cancer. The model is a five dimensional system of the first order of ordinary differential equations that represents the interaction between the free Human Papilloma Virus (HPV) population and four cells sub-populations, i.e., the normal cells, infected cells by HPV, precancerous cells, and cancer cells. We focus our analysis to determine the existence conditions of the nontrivial equilibrium point, the bifurcations, and the sensitivity of the parameters that play important roles in metastasis. Based…