Mathematical Biosciences

A mathematical model for two strains of Malaria and Cholera with optimal control is studied and analyzed to assess the impact of treatment controls in reducing the burden of the diseases in a population, in the presence of malaria drug resistance. The model is shown to exhibit the dynamical property of backward bifurcation when the associated reproduction number is less than unity. The global asymptotic stability of the disease-free equilibrium of the model is proven not to exist. The necessary ...

Platelets have been seen traditionally as fragments of blood mediating coagulation. However, evidence during malaria infection suggests that platelets also act against merozoites, an infectious form of malaria in the bloodstream, and megakaryocytes can release giant platelets with a larger volume than normal platelets. We propose a mathematical model to study the interaction between red blood cells, merozoites, and platelets during malaria infection. We analyzed two cases of the interaction of p...

Malaria prevalence in sub-Saharan Africa remains high. Kenya for example, records about 3.5 million new cases and 11 thousand deaths each year [1]. Most of these cases and deaths are among children under five. The main control method in malaria endemic regions has been through the use of pyrethroid-treated bed nets. Although this approach has been fairly successful, the gains are threatened by mosquito-resistance to pyrethroids, physical and chemical degradation of ITNs that reduce their efficac...

The recent emergence and established presence of Aedes aegypti in the Autonomous Region of Madeira, Portugal, was responsible for the first autochthonous outbreak of dengue in Europe. The island has not reported any dengue cases since the outbreak in 2012. However, there is a high risk that an introduction of the virus would result in another autochthonous outbreak given the presence of the vector and permissive environmental conditions. Understanding the dynamics of a potential epidemic is crit...

COVID-19 (Coronavirus Disease-2019) is an international public health problem with a high rate of severe clinical cases. Several treatments are currently being tested worldwide. This paper focuses on anti-malarial drugs such as chloroquine or hydroxychloroquine. We compare the dynamics of COVID-19 daily deaths in countries using anti-malaria drugs as a treatment from the start of the epidemic versus countries that do not, the day of the 3rd death and the following 10 days. We then use a ARIMA mo...

Malaria is still a life threatening parasitic disease due to the change in environmental and socio-economic conditions. This paper introduces a novel mathematical model to study the impact of drug-resistant strain, recovered-carrier, and relapse on malaria dynamics by implementing Caputo-Fabrizio fractional order derivative (CFFOD). We begin by presenting theoretical results that are derived for our model. We also derive the expression for the control reproduction number and investigate the equi...

Experimental evidence confirms that interleukin-10 plays a critical role in clearing acute hepatitis B virus infection. This paper aims to develops a mathematical model to explore the dynamics of how the immune system responds to hepatitis B virus (HBV) and coexisting liver cancer within the liver cell population. Unlike previous models; we categorize liver cells into various stages of infection. We determine the invasion probability for transmission dynamics, specifically the basic reproduction...

In a recent paper Zhang et al. [1] elegantly incorporate the evolution of inter-host virus fitness into an epidemiological model. They show that this leads to substantial changes in the system dynamics and in particular that evolution can "rescue" the pathogen population if the mutation rate is high enough. However, their model rests on the assumption that mutations that affect inter-host fitness are neutral on average. Here we show that under more realistic assumptions concerning the fitness di...

We study a novel multi-strain SIR epidemic model with selective immunity by vaccination. A newer strain is made to emerge in the population when a preexisting strain has reached equilbrium. We assume that this newer strain does not exhibit cross-immunity with the original strain, hence those who are vaccinated and recovered from the original strain become susceptible to the newer strain. Recent events involving the COVID-19 virus demonstrates that it is possible for a viral strain to emerge from...

We estimate the basic reproduction number[R] 0 and the overdispersion parameter[K] at two regions in Indonesia: Jakarta-Depok and Batam. Based on the first 1288 confirmed cases in both regions, we find a high degree of individual-level variation in the transmission. The basic reproduction number[R] 0 is estimated at 6.79 and 2.47, while the overdispersion parameter[K] of a negative-binomial distribution is estimated at 0.06 and 0.2 for Jakarta-Depok and Batam, respectively. This suggests that su...

We present a dynamical model of the onset and severity of cyclical epidemic disease taking account only of seasonal boosts of antibody during the infectious season and residual immunity remaining from one season to the next. We also compile data from public health sources on the annual number of cases of influenza A and peak infectivity month over a quarter century. In these data, we discover that there is a negative correlation between the change in number of cases from one year to the next and...

Herd immunity refers to the collective resistance of a population against the spreading of an infection as an epidemic. Understanding the dependencies of herd immunity on various epidemiological parameters is of immense importance for strategizing control measures against an infection in a population. Using an age-dependent branching process model of infection propagation, we obtain interesting functional dependencies of herd immunity on the incubation period of the contagion, contact rate, and ...

The COVID-19 pandemic has sparked significant interest in developing mathematical models that capture more of the complexities of the dynamics of disease transmission and control. In this study, we presented a deterministic compartmental model for the transmission of COVID-19. The model has eight compartments: susceptible, exposed, asymptomatic, unreported symptomatic, reported symptomatic, hospitalised, recovered, and dead. Individuals in each compartment are discretised into age and deprivatio...

We model and calculate the fraction of infected population necessary for herd immunity to occur, taking into account the heterogeneity in infectiousness and susceptibility, as well as the correlation between the two parameters. We show that these cause the reproduction number to decrease with progression, and consequently have a drastic effect on the estimate of the necessary percentage of the population that has to contract the disease for herd immunity to be reached. We discuss the implication...

Growth and aging are fundamental features of animal life. The march from fertilization to oblivion comes in enormous variety: days and hundreds of cells for nematodes, decades and trillions of cells for humans.1-4 Since Verhulst (18385) proposed the Logistic Equation - exponential growth with a countervailing linear decline in rate - biologists have searched for ever better density-dependent growth equations,6-12 none of which accurately capture the relationship between size and time for real an...

Chagas disease, also known as American trypanosomiasis, is caused by a protozoan blood-borne pathogen called Trypanosoma cruzi. The World Health Organization (WHO) has classified Chagas as one of 21 neglected tropical diseases present in the world and estimates that 6-7 million people are currently infected with Chagas. Congenital transmission of Chagas disease contributes to a significant amount of new infections, especially in endemic areas where 22.5% of new infections are due to congenital t...

This paper looked at the exploration of Lassa fever transmission dynamics through stochastic models which yielded valuable insights into the interplay of factors influencing the probability of extinction and persistence of the virus within a population. By embracing the inherent randomness and variability in the system, the model provided a more realistic representation of the complex ecological and epidemiological dynamics of Lassa fever. We developed the deterministic model using a system of o...

The investigation of epidemiological scenarios characterized by chaotic dynamics is crucial for understanding disease spread and improving disease control strategies. Motivated by dengue fever epidemiology, in this study we introduce the SIRSIR-UV model, which accounts for differences between primary and secondary infections and explicit disease vector dynamics. Our analysis, employing nonlinear dynamics and bifurcation theory, provides key insights into how vectors contribute to the overall sys...

Human movement is a key factor in infectious diseases spread such as dengue. Here, we explore a mathematical modeling approach based on a system of ordinary differential equations to study the effect of human movement on characteristics of dengue dynamics such as the existence of endemic equilibria, and the start, duration, and amplitude of the outbreak. The model considers that every day is divided into two periods: high-activity and low-activity. Periodic human movement between patches occurs ...

We develop a stochastic, multi-strain, compartmental epidemic model to estimate the relative transmissibility and immune escape of the Omicron variant of concern (VOC) in South Africa. The model integrates population, non-pharmaceutical interventions, vaccines, and epidemiological data and it is calibrated in the period May 1st, 2021 - November 23rd, 2021. We explore a parameter space of relative transmissibility with respect to the Delta variant and immune escape for Omicron by assuming an init...