Journal of Biological Dynamics

We consider a Darwinian (evolutionary game theoretic) version of a standard susceptible-infectious SI model in which the resistance of the disease causing pathogen to a treatment that prevents death to infected individuals is subject to evolutionary adaptation. We determine the existence and stability of all equilibria, both disease-free and endemic, and use the results to determine conditions under which the treatment will succeed or fail. Of particular interest are conditions under which a successful treatment in the absence of resistance adaptation (i...

Steady states of dynamical systems, whether stable or unstable, are critical for understanding future evolution. Robust steady states, ones that persist under small changes in the model parameters, are desired when modelling ecological systems, where it is common for accurate and detailed information on functional form and parameters to be unavailable. Previous work by Jahedi et al. [ Robustness of solutions of almost every system of equations , SIAM J. Appl. Math. 82(5) (2022), pp. 1791-1807; Structured systems of nonlinear equations , SIAM J...

Populations are generally censused daily, weekly, monthly or annually. In this paper, we introduce a discrete-time nutrients-phytoplankton-oysters (NPO) model that describes the interactions of nutrients, phytoplankton and oysters in a bay ecosystem. We compute the threshold parameter <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mi>N</mml:mi></mml:msub></mml:math> for persistence of phytoplankton with or without oysters...

Atherosclerosis is a leading cause of death worldwide. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation. Diabetic patients are twice as likely to have a heart attack or stroke. In this paper, we consider a simplified mathematical model for diabetic atherosclerosis involving LDL, HDL, glucose, insulin, free radicals (ROS),  β cells, macrophages and foam cells, which satisfy a system of partial differential equations with a free boundary, the interface between the blood flow and the plaque...

Despite the existence of a powerful theoretical foundation for the development of multiscale models of infectious disease dynamics in the form of the replication-transmission relativity theory, the majority of current modelling studies focus more on single-scale modelling. The explicit aim of this study is to change the current predominantly single-scale modelling landscape in the design of planning frameworks for the control, elimination and even eradication of infectious disease systems through the exploitation of multiscale modelling methods based on the application of the replication-transmission relativity theory...

The growth rate of a population serves as a measure of its Darwinian fitness, while its sensitivity indicates the intensity of selection. Generally, the sensitivity of r decreases with age, resulting in an expected increase in population mortality over time. However, this does not hold true for many populations, especially those exhibiting negative senescence. Both evolutionary entropy and its sensitivity serve as complementary measures for assessing fitness and the intensity of selection. The sensitivity of entropy is typically a convex function of age, implying stronger selection pressures in younger and older age groups...

A computational approach is adapted to analyze the parameter identifiability of a compartmental model. The model is intended to describe the progression of the COVID-19 pandemic in Chile during the initial phase in early 2020 when government declared quarantine measures. The computational approach to analyze the structural and practical identifiability is applied in two parts, one for synthetic data and another for some Chilean regional data. The first part defines the identifiable parameter sets when these recover the true parameters used to create the synthetic data...

This paper aims to apply an optimal control theory for the autonomous model of the leptospirosis epidemic to examine the effect of four time-dependent control measures on the model dynamics with cost-effectiveness. Pontryagin's Maximum Principle was used to derive the optimality system associated with the optimal control problem. Numerical simulations of the optimality system were performed for different control strategies and the results were presented graphically with and without controls. The optimality system was simulated using the Forward-Backward Sweep method in the Matlab programme...

The COVID-19 epidemic has been spreading around the world for nearly three years, and asymptomatic infections have exacerbated the spread of the epidemic. To analyse and evaluate the role of asymptomatic infections in the spread of the epidemic, we establish an improved COVID-19 infectious disease dynamics model. We fit the epidemic data in the four time periods corresponding to the selected 614G, Alpha, Delta and Omicron variants and obtain the proportion of asymptomatic persons among the infected persons gradually increased and with the increase of the detection ratio, the cumulative number of cases has dropped significantly, but the decline in the proportion of asymptomatic infections is not obvious...

We provide a procedure for deriving discrete population models for the size of the adult population at the beginning of each breeding cycle and assume only adult individuals reproduce. This derivation technique includes delay to account for the number of breeding cycles that a newborn individual remains immature and does not contribute to reproduction. These models include a survival probability (during the delay period) for the immature individuals, since these individuals have to survive to reach maturity and become members of, what we consider, the adult population...

Dengue fever creates more than 390 million cases worldwide yearly. The most effective way to deal with this mosquito-borne disease is to control the vectors. In this work we consider two weapons, the endosymbiotic bacteria Wolbachia and predators of mosquito larvae, for combating the disease. As Wolbachia -infected mosquitoes are less able to transmit dengue virus, releasing infected mosquitoes to invade wild mosquito populations helps to reduce dengue transmission. Besides this measure, the introduction of predators of mosquito larvae can control mosquito population...

Worldwide, the recent SARS-CoV-2 virus disease outbreak has infected more than 691,000,000 people and killed more than 6,900,000. Surprisingly, Sub-Saharan Africa has suffered the least from the SARS-CoV-2 pandemic. Factors that are inherent to developing countries and that contrast with their counterparts in developed countries have been associated with these disease burden differences. In this paper, we developed data-driven COVID-19 mathematical models of two 'extreme': Cameroon, a developing country, and New York State (NYS) located in a developed country...

This paper studies a 2-dimensional discrete-time competition model of Ricker type with reproductive delay. The model is examined under the assumption that species 1 and 2 have the same properties except that a fraction η of species 1 individuals delays the initiation of reproduction. This assumption ensures that species 1 is dominated by species 2 in the sense that species 2 is increasing whenever species 1 is increasing. It is shown that, even under this assumption, delayed reproduction can be adaptive, i...

We propose a discrete-time host-parasitoid model with stage structure in both species. For this model, we establish conditions for the existence and global stability of the extinction and parasitoid-free equilibria as well as conditions for the existence and local stability of an interior equilibrium and system persistence. We study the model numerically to examine how pesticide spraying may interact with natural enemies (parasitoids) to control the pest (host) species. We then extend the model to an impulsive difference system that incorporates both periodic pesticide spraying and augmentation of the natural enemies to suppress the pest population...

We propose a hand, foot and mouth disease (HFMD) transmission model for children with behaviour change and imperfect quarantine. The symptomatic and quarantined states obey constant behaviour change while others follow variable behaviour change depending on the numbers of new and recent infections. The basic reproduction number <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub></mml:math> of the model is defined and shown to be a threshold for disease persistence and eradication...

We develop and investigate a discrete-time predator-prey model with cooperative hunting among predators and a spatial prey refuge. The system can exhibit two positive equilibria if the magnitude of cooperation is large and the maximal reproduction number of predators is less than one. In such a scenario, the predator population may exhibit a strong Allee effect, and therefore the predator may survive if its density is above the threshold. When the positive equilibrium is unique, we prove that hunting cooperation can destabilize the equilibrium through a Neimark-Sacker bifurcation...

People's lifestyles play a major role in disease risk. Some employment sectors and transport modes involve fixed exposures regardless of community size, while in other settings exposure tracks with population density. MERS-CoV, a coronavirus discovered in Saudi Arabia in 2012 closely related to those causing SARS and COVID-19, appears to need extended contact time for transmission, making some segments of a community at greater risk than others. We model mathematically how heterogeneity in contact rate structure impacts disease spread, using as a case study a MERS outbreak in two Saudi Arabian communities...

A stochastic mathematical model is proposed to study how environmental heterogeneity and the augmentation of mosquitoes with <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>W</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>h</mml:mi><mml:mi>i</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:math> bacteria affect the outcomes of dengue disease...

A multi-patch HIV/AIDS model with heterosexual transmission is formulated to investigate the impact of population migration on the spread of HIV/AIDS. We derive the basic reproduction number <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math> and prove that if <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:math>, the disease-free equilibrium is globally asymptotically stable...

In this work, we first modify a Lotka-Volterra predator-prey system to incorporate an opportunistic predator and weak Allee effect in prey. The prey will be extinct if the combined effect of hunting and other food resources of predator is large. Otherwise, the dynamic behaviour of the system is extremely rich. A series of bifurcations such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation can happen. The validity of the theoretical results are supported with numerical simulations...